Dna-based neural network

ABSTRACT

An analog signal processing circuit comprising: a first promoter operably linked to a nucleic acid sequence encoding a first output molecule, wherein said promoter is responsive to a cooperative input signal comprising at least two cooperative inputs, and wherein expression of said at least two cooperative inputs is tunable.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/525,242, filed Jun. 27, 2017, and entitled “MACHINELEARNING ALGORITHM AND USES THEREOF”, the content of which isincorporated herein by reference in its entirety.

FIELD OF INVENTION

The present invention is directed to computer program products in thefield of machine learning and synthetic biology.

BACKGROUND OF THE INVENTION

Biological systems are comprised of remarkable parallel and distributedcomputing networks with adaptive, self-repairing and replicativecapacities in performance of real-world tasks. Scientists and engineershave been inspired to mimic these features in design of artificialintelligent systems. For example, neuromorphic computing appliesabstract models of neural systems, such as the perceptron, usingmicroelectronics, to build intelligent machines. However, because theneuromorphic computing discipline demands a deep understanding ofbiological mechanisms in brains, the field has progressed slowly.

During the past decade, researchers have successfully appliedbiophysical models to create basic biological networks with predictablebehaviors in living cells, and have shown that biological networks areconstructed from only a few types of design patterns that areimplemented with different genes. At the same time, significantadvancements in genomic DNA engineering and assembly techniques havebeen achieved, subsequently laying down an extraordinary set of designrules proposed to explain the complexity of biological systems and whichhave been exploited to construct synthetic gene networks in livingcells. These rules are mostly inspired by computer and electricalengineering concepts. For example, several biological networks have beenshown to act in an ‘AND-logic-gate’ manner to control promoter activitywhile others synthesize a toggle switch in bacteria. However, signals inliving cells are stochastic (noisy) and analog (graded) in nature, suchthat digital logic abstraction is often an oversimplified means ofcapturing design features. Thus, the challenge remains in scaling-upgene networks, increasing biological robustness, and building adaptivebiological systems, in view of cellular resource limitations, adeficiency of orthogonal genetic devices, and lack of simple learningmechanisms. Recently, it was shown that synthetic gene circuits can beengineered to execute analog computational functions in living cells.Such gene circuits exploit feedback loops to perform logarithmicallylinear sensing, addition, ratio-meter, and power-law computations. Thesecircuits involve fewer components and execute more complex operationsthan their digital counterparts. In the same context, it has been shownthat biological systems can be mapped to ultra-low-power analogtranslinear electronics systems, which is termed cytomorphics. Forexample, regulation of gene expression can be modeled by networks ofsubthreshold MOS (Metal-Oxide-Semiconductor) transistors.

Biological architectures in living cells contain extensively noisy,imprecise, and unreliable analog parts that collectively interactthrough analog and digital signals to solve interactively noise-tolerantparallel tasks online with astoundingly low power consumption, vastlyexceeding the characteristics of present-day computers. For example, asingle cell in the body performs 10⁷ biochemical reactions per secondfrom its noisy molecular inputs, expending less than 1 pW¹⁹.Furthermore, neural and molecular networks both use bit streamdata-encoding pulses (spikes in neuron and mRNA transcript in cellbiology) for processing and transcommunicating. Additionally, bothsystems use naturally graded signals for computation (post-synapticpotential in neurons or translation of mRNA to protein concentration incell biology). Furthermore, both system types are composed of similarcomplex networks topologies (e.g. feed-forward, negative and positivefeedbacks) and highly interconnected nodes. Both systems have two typesof activation and repression and are adaptive to new environmentalconditions by employing learning and evolution mechanisms.

SUMMARY

The following embodiments and aspects thereof are described andillustrated in conjunction with systems, tools and methods which aremeant to be exemplary and illustrative, not limiting in scope.

There is provided, in accordance with an embodiment, an analog signalprocessing circuit comprising: a first promoter operably linked to anucleic acid sequence encoding a first output molecule, wherein thepromoter is responsive to a cooperative input signal comprising at leasttwo cooperative inputs, and wherein expression of the at least twocooperative inputs is tunable.

In some embodiments, the cooperativity of the at least two inputs istunable.

In some embodiments, the first promoter is a hybrid promoter comprisingat least two transcriptional-regulator binding sites.

In some embodiments, at least one of the at least two regulator bindingsites binds an activator and at least one of the at least two regulatorbinding sites binds a repressor.

In some embodiments, the at least two inputs bind to the at least tworegulator binding sites, or the at least two inputs bind to at least tworegulators that bind to the at least two regulator binding sites.

In some embodiments, the at least two regulator binding sites are a LuxRbinding site and a LacI binding site.

In some embodiments, the at least two inputs are acyl-homoserine lactone(AHL) and isopropyl β-d-thiogalactopyranoside (IPTG).

In some embodiments, the analog signal processing further comprises asecond promoter operably linked to a nucleic acid sequence encoding atleast one of the cooperative inputs, wherein the second promotercomprises a binding site for the at least one of the cooperative inputs.

In some embodiments, the binding site in the second promoter comprises amodification that alters a binding affinity of the at least onecooperative input to the binding site relative to a binding affinity ofthe at least one cooperative input to an unmodified binding site.

In some embodiments, a binding affinity to the first promoter of the atleast two inputs, or the at least two regulators bound to the inputs, istunable.

In some embodiments, the analog signal processing circuit furthercomprises a third promoter operably linked to a nucleic acid sequenceencoding a second output molecule, wherein the third promoter isresponsive to the first output molecule.

In some embodiments, the third promoter comprises a pBAD promoter, andthe first output molecule is araC protein.

In some embodiments, the analog signal processing circuit furthercomprises arabinose.

In some embodiments, the analog signal processing circuit furthercomprises: (a) a regulatory sequence that regulates translation of thefirst output molecule and is located between the first promoter and thenucleic acid sequence encoding the first output molecule; (b) aregulatory sequence that regulates translation of the second outputmolecule and is located between the third promoter and the nucleic acidsequence encoding the second output molecule; or both (a) and (b).

In some embodiments, the regulatory sequence is a riboswitch responsiveto theophylline.

In some embodiments, the first promoter is responsive to a protein orprotein complex consisting of more than one subunit, wherein the atleast two cooperative inputs are at least two of the subunits.

In some embodiments, the protein consisting of more than one subunit isT7 RNA polymerase and the at least two cooperative inputs are analpha-fragment subunit of T7 RNA polymerase, a sigma-fragment subunit ofT7 RNA polymerase and a beta-core fragment subunit of T7 RNA polymerase.

In some embodiments, the analog signal processing circuit furthercomprises a nucleic acid sequence coding for the alpha-fragment subunit,a nucleic acid sequence coding for the sigma-fragment subunit and anucleic acid sequence coding for the beta-core fragment subunit, whereinthe nucleic acid sequences coding for the T7 RNA polymerase subunits areoperably linked to at least one promoter.

In some embodiments, the nucleic acid sequences coding for the T7 RNApolymerase subunits are operably linked to a plurality of promoters,wherein all three nucleic acid sequences are not linked to the samepromoter, and wherein the cooperativity of the inputs is determined bythe binding affinities of the plurality of promoters.

In some embodiments, the protein consisting of more than one subunit isCas9.

In some embodiments, the at least two cooperative inputs are Cas9 and asmall guide RNA (sgRNA).

In some embodiments, the tunability of the Cas9 and the sgRNA isdetermined by mutating the sgRNA sequence to alter a binding affinity ofthe Cas9 to the sgRNA.

In some embodiments, the at least two cooperative inputs are at leasttwo factors that share a common binding site, and wherein the firstpromoter comprises the common binding site.

In some embodiments, the analog signal processing circuit of the presentinvention further comprises the at least two factors that share a commonbinding site.

In some embodiments, the at least two factors that share a commonbinding site are a Sigma factor and an anti-Sigma factor.

In some embodiments, the first promoter operably linked to a nucleicacid sequence encoding a first output molecule further comprises afourth promoter that transcribes in a direction opposite to atranscriptional direction of the first promoter, wherein binding of atleast one of the at least two cooperative inputs to the fourth promoterinterferes with transcription from the first promoter.

There is also provided, in accordance with an embodiment, an analogsignal processing circuit comprising: (a) a first tunable promoteroperably linked to a nucleic acid sequence coding for a DNA recombinase;(b) a second constitutive promoter operably linked to a nucleic acidsequence that, when inverted, codes for a first output molecule, whereinthe nucleic acid sequence is flanked by recognition sites for the DNArecombinase; and (c) decoy recognition sites for the DNA recombinase,wherein said decoy sites are within (i) a nucleic acid moleculecomprising (a), (ii) a nucleic acid molecule comprising (b), or (iii) athird nucleic acid molecule.

In some embodiments, the tunable promoter comprises a Plux binding site,and is tunable by addition of AHL.

In some embodiments, the circuit converts an analog signal into adigital output.

In some embodiments, the circuit further comprises a cell which enclosesthe components of the system.

In some embodiments, the cell is selected from a prokaryotic or aeukaryotic cell.

In some embodiments, the output molecule is a fluorescent molecule.

There is also provided, in accordance with an embodiment, a cellcomprising the analog signal processing circuit of the presentinvention.

There is further provided, in accordance with an embodiment, a methodfor converting an analog signal into a digital output, comprisingcontacting the analog signal processing circuit of the presentinvention, or the cell of the present invention, with the at least twoinputs and detecting the first output molecule, the second outputmolecule, or both thereby converting an analog signal into a digitaloutput.

In some embodiments, the detecting comprises quantification of theoutput molecule.

In some embodiments, the digital output is either a positive or anegative output.

In some embodiments, the method further comprises tuning a threshold forconverting the analog input into a positive digital output.

In some embodiments, the tuning comprises at least one of: tuningexpression of at least one of the at least two regulators; tuning abinding efficiency of at least one of the at least two inputs to abinding site; tuning a binding efficiency of at least one of the atleast two regulators to a binding site; adding a molecule that binds tothe regulatory sequence; and adding a molecule that binds to the firstoutput molecule and alters binding of the first output molecule to thethird promoter.

In some embodiments, the molecule that binds the regulatory sequence istheophylline.

In some embodiments, the molecule that binds to the first outputmolecule is arabinose.

There is further provided in accordance with an embodiment, a systemcomprising at least one hardware processor; and a non-transitorycomputer-readable storage medium having stored thereon programinstructions, the program instructions executable by the at least onehardware processor to execute a genetic-type machine learning algorithmconfigured for: receiving a sequence of inputs, wherein each of saidinputs has an associated weight, operating a neural network to generate,as output, a weighted multiplication of said inputs, calculating anerror value between said output and a target output, and adjusting thevalues of one or more of said weights based on said error value and aspecified learning rate, wherein said adjusting is determined, at leastin part, based on a log-linear gradient descent training rule.

There if further provided in accordance with an embodiment, a methodcomprising operating at least one hardware processor for executing agenetic-type machine learning algorithm configured for: receiving asequence of inputs, wherein each of said inputs has an associatedweight, operating a neural network to generate, as output, a weightedmultiplication of said inputs, calculating an error value between saidoutput and a target output, and adjusting the values of one or more ofsaid weights based on said error value and a specified learning rate,wherein said adjusting is determined, at least in part, based on alog-linear gradient descent training rule.

There if further provided in accordance with an embodiment, a computerprogram product comprising a non-transitory computer-readable storagemedium having program instructions embodied therewith, the programinstructions executable by at least one hardware processor to execute agenetic-type machine learning algorithm configured for: receiving asequence of inputs, wherein each of said inputs has an associatedweight, operating a neural network to generate, as output, a weightedmultiplication of said inputs, calculating an error value between saidoutput and a target output, and adjusting the values of one or more ofsaid weights based on said error value and a specified learning rate,wherein said adjusting is determined, at least in part, based on alog-linear gradient descent training rule

In some embodiments, the hardware processor is a DNA-based processor.

In some embodiments, the algorithm is further configured to repeatiteratively said steps of operating, calculating, and adjusting, untilsaid error value is less than a specified threshold.

In some embodiments, the neural network comprises a plurality of layers.In some embodiments, said adjusting further comprises backpropagatingsaid gradient descent through said plurality of layers, using the chainrule derivatives.

In some embodiments, said calculating comprises determining a meansquare error value.

In some embodiments, said learning rate is an adaptive learning rate.

In addition to the exemplary aspects and embodiments described above,further aspects and embodiments will become apparent by reference to thefigures and by study of the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments are illustrated in referenced figures. Dimensionsof components and features shown in the figures are generally chosen forconvenience and clarity of presentation and are not necessarily shown toscale. The figures are listed below.

FIGS. 1A-F: (1A) anatomical structure of the perceptron, (1B) shiftedsigmoid function, (1C) shifted sigmoid function in a log-linear domainfits a Michaelis-Menten model, (1D) three main models of cooperativityin living cells, (1E) anatomical structure of the perceptgene, and (1F)simulation results of the perceptgene using a signum activationfunction;

FIGS. 2A-H: (2A) & (2B) construction and experimental results of agenetic analog multiplier based on a hybrid promoter in E. coli, (2C) &(2D) construction and experimental results of a genetic analogmultiplier based on a riboswitch in E. coli, (2E) & (2F) constructionand experimental results of a perceptgene in E. coli, (2G) simulationresults of summation, and (2H) simulation results of the perceptron;

FIGS. 3A-F: (3A) PF and shunt circuit for linearization, (3B) & (3C)proposed analog multiplier based on T7 RNAp and CRISPR system,respectively, (3D) PF and shunt circuit for cooperativity weightfine-tuning, (3E) Control of the threshold of the perceptgene based oncompetition between promoters, and (3F) Control of the threshold of theperceptgene based on decoy binding sites;

FIGS. 4A-D: (4A) and (4B) mapping SMN to ANN, the NF and PF in the SMNare used to tune cooperativity, (4C) stochastic simulation results ofthe perceptgene when intrinsic noise is added to the multiplication ofEquation 3, and (4D) Stochastic simulation results of the perceptronwhen intrinsic noise is added to the summation of the equation, and alog-linear activation function is used;

FIGS. 5A-E: (5A) the learning algorithm-based perceptgene model, (5B) &(5C) construction of an OR logic gate, based on the perceptron andperceptgene, (5D) simulation results of perceptron training, using theAdaline algorithm and perceptgene training using the Adalogline to learnOR logic functions (learning rate for both systems 0.04), and (5E)simulation results of perceptron (Adaline algorithm) and of theperceptgene (Adalogline algorithm) to learn an OR logic function whenintrinsic noise is added to the output of the both system;

FIGS. 6A-D: (6A) the basic structure of a Hopfield molecular network(HMN) based on a perceptgene model, (6B) analog trans-linearsubthreshold MOS circuit demonstrating an HMN, (6C) a log-linearanalog-to-digital converter (ADC), and (6D) A schematic model of theenergy landscape in the vicinity of the global minima for two analoginput voltages;

FIGS. 7A-H: (7A) implementation of elementary logic gates using a linearthreshold (LTU) model, (7B) truth table of 1-bit full adder, (7C) fullbit adder outputs as a function of the analog multiplication signal,(7D) implementation of a 1-bit full adder using a log-linear threshold(L²TU) model, (7E) construction and results of a linear-logdigital-to-analog converter in living cells, (7F) & (7G) constructionand experimental results of log-linear analog-to-digital converterprocessing unit to implement low/band/high pass circuits in E. coli, and(7H) experimental results of cell-to-cell communication using AHL quorumsensing molecules;

FIGS. 8A-B: (8A) distribution number of protein subunits in E. coli, and(8B) Shannon model for a perceptgene in the presence of intrinsic noisewithin the biochemical reaction; and

FIGS. 9A-9G illustrate experimental results;

FIG. 10 A line graph showing comparative experimental results of pg andpp MINIST test results 60000 train 10000 test batch 100 learning rate0.01.

DETAILED DESCRIPTION OF THE INVENTION

Disclosed herein are a system and a method which provide for syntheticgene networks in living cells that can demonstrate the computationalabilities of neural networks. The present invention provides for themapping of neural networks to molecular biological and nanoelectronicnetworks, using a simple mathematical transformation. The disclosedapproach may be configured for providing a novel computational frameworkthat inherently exists in synthetic gene networks and is implemented bytranslinear analog circuits and memristor devices to build adaptivesystems with emergent collective parallel computational abilities inelectronics and living cells.

The present invention is based, at least in part, on the notion thatartificial neural networks (ANNs) are a set of theoretical abstractmodels inspired by neurobiological networks. ANNs have been proposed asa powerful computational framework for translation of interactivecognitive tasks that the human brain appears to solve relatively easilyas compared to a conventional computer, such as content addressablememory, pattern classification, object recognition, functionapproximation, and optimizations solving. ANNs use simple-unreliableanalog-weighted elements that collectively interact through non-linearfunctions, which act to achieve reliable decision-making. Theinteractions between non-linear functions (nodes) through the analogconnections (weights) lead to global behavior of the network, whichcannot be observed only by the node elements. The second key feature ofANN is its plasticity—the ability to learn and adapt to new patternsbased on dataset history (information) compressed within the analogweights, which are periodically updated.

The perceptron, which is the basic computational element in ANNs, is anabstract model that can capture the computational power of biologicalneurons. Because biological and neural architectures share manyfeatures, a simple transformation between the basic computationalstructure of perceptron and molecular processing unit can be discerned.Accordingly, an interaction between proteins and DNA that controls thepromoter activity (P_(r), comprising a region of DNA that initiatestranscription of a particular gene) can be viewed either as a node or asan activation function which, in turn, can be simply described by aMichaelis-Menten model.

In analogy to the perceptron, it may be assumed that the activity of thepromoter in DNA is a signum function. However, in natural and syntheticsystems, it is approximated as a log-linear sigmoid function(Hill-function). In some embodiments, the present framework, termed‘perceptgene,’ may be modeled on this framework. The perceptgene isinspired by molecular biology and has a computational process identicalto that of the perceptron, i.e., consisting of three operations: (i)multiplication of all the inputs in analog fashion; this process ismainly implemented by binding reactions, (ii) each input (x_(i)) isinvoked by a power law function with a coefficient n_(i) that representsthe cooperativity binding reaction, and (iii) a log-linear activationfunction that is implemented by promoter activity or a bio-enzymaticreaction (thresholding).

The present framework is inspired by neural biology, which is inherentlypresent in cellular biology, to build intelligent parallel processingbiological systems. In contrast to most current approaches, whichemphasize digital paradigms of thought by building artificial logicgates, counter, discrete quantizer and memory devices in living cells,the disclosed framework can execute sophisticated analog computationaland learning (evolutionary) functions in concert with decision-makingdigital circuits within living cells. In some embodiments, the presentframework may provide for an intelligent adaptive-robust-parallelcomputing synthetic biological systems that set constraints on energyand host cell resources. In addition, in some embodiments, the presentframework may be able to leverage the multidisciplinary nature ofcytomorphics to interpolate/extrapolate principles of molecular networksinto engineering, and vice versa, just as neuromorphic engineering hasled to biologically inspired engineered systems.

As noted above, because signals in living cells are stochastic (noisy)and analog (graded) in nature, digital logic abstraction is often anoversimplified means of capturing design features. Some of thelimitations of analog frameworks include noise sensitivity, low dynamicrange, lack of design standards, exhaustive manual design flow and longtime-to-market, large developing costs and human resources.

Accordingly, in some embodiments, the present framework provides fornovel adaptive synthetic biological systems and collective emergentelectronic circuits that operate precisely and with minimal energyrequirements. Such systems may be utilized in many fields and areas, byinterpolating new applications, such as comprehensive study of complexbiological systems (e.g., mutations involved in cancer, see Loeb K R,Loeb L a. Significance of multiple mutations in cancer. Carcinogenesis.2000; 21(3):379-385. doi:10.1093/carcin/21.3.379); embedded electronicsystems for big data processing in healthcare (see Foster K R, KoprowskiR, Skufca J D. Machine learning, medical diagnosis, and biomedicalengineering research—commentary. Biomed Eng Online. 2014; 13(1):94.doi:10.1186/1475-925X-13-94); and ultra-low power systems design forbiomedical applications (e.g., low-cost microelectronics with equallylow-cost genetically engineered microbial sensors; see Sarpeshkar R.Ultra Low Power Bioelectronics: Fundamentals, Biomedical Applications,and Bio-Inspired Systems; 2010.doi:http://dx.doi.org/10.1017/CB09780511841446; Daniel R, Almog R, RonA, Belkin S, Shachm-Diamand Y. Modeling and Measurement of a Whole-cellBioluminescent Biosensor Based on a Single Photon Avalanche Diode.Biosensors and Bioelectronics 2008; 24 (882)). The present systems mayalso be configured for setting the fundamental understanding andcompetent engineering tools required to build an intelligent hybridmachine-organism system (e.g., to develop bio-classifiers for detectionof disease that are connected via the Internet-of-Things, see Gubbi J,Buyya R, Marusic S, Palaniswami M. Internet of Things (IoT): A vision,architectural elements, and future directions. Futur Gener Comput Syst.2013; 29(7):1645-1660. doi:10.1016/j.future.2013.01.010).

In some embodiments, the present invention provides for a novel abstractmolecular cell biology model, termed ‘perceptgene,’ equivalent to theperceptron model which is widely used in artificial neural networks(ANNs) (see, e.g., Rosenblatt F. The Perceptron—A Perceiving andRecognizing Automaton. Rep 85, Cornell Aeronaut Lab. 1957:460-461.doi:85-460-1; Mackay D J C. Information Theory, Inference, and LearningAlgorithms. Learning. 2003; 22(3):348-349.doi:10.1017/S026357470426043X). This novel model will be inherentlyimplemented in gene networks to construct synthetic molecular networks(SMNs), as well as in translinear electronic circuits to buildartificial molecular networks (AMNs).

In some embodiments, the present invention may be configured fordeveloping an alternative learning algorithm based on the perceptgenemodel, by optimizing the output error using gradient descent in alog-linear domain. The present invention may then be configured forbeing concurrently applied in SMNs and AMNs to build adaptive biologicalsystems with evolutionary abilities and ultra-low power bioinspiredtranslinear electronic circuits for supervised learning big-dataapplications.

In some embodiments the present invention may be configured fordeveloping an alternative model of the Hopfield energy function (see,e.g., Hopfield J J. Neural networks and physical systems with emergentcollective computational abilities. Proc Natl Acad Sci USA. 1982;79(8):2554-2558. doi:10.1073/pnas.79.8.2554 33), relying on theperceptgene model in a log-linear domain. This may then be applied inSMNs and AMNs to build biological and electronics systems with parallelcomputational abilities (Boltzmann machine; see, e.g., Hinton G, HintonG, Sejnowski T, Sejnowski T. Learning and Relearning in BoltzmannMachines. Vol 1; 1986).

In some embodiments, the present invention may be configured fordeveloping an alternative model of the linear threshold unit model,relying on the perceptgene model in a log-linear model. This may then beapplied in SMNs to scale gene networks in living cells. Furthermore, theperceptgene model may be utilized to study the architecture of genenetworks in natural biological systems for scaling syntheticbio-inspired systems.

In some embodiments, the present invention provides for an analog signalprocessing circuit comprising a first promoter operably linked to anucleic acid sequence encoding a first output molecule, wherein thepromoter is responsive to a cooperative input signal. In otherembodiments, the present invention provides for a cell comprising theanalog signal processing circuit of the invention. In yet otherembodiments, the present invention provides for a method for convertingan analog signal into a digital output, comprising contacting the analogsignal processing circuit of the invention or a cell of the inventionwith a cooperative input signal and detecting at least one outputmolecule, thereby converting an analog signal into a digital output.

As used herein, an “analog signal” refers to any input with at least oneparameter that varies in magnitude. It will be understood by one skilledin the art, that an analog signal is not a signal that is either presentor absent, but rather a signal that when present has a variablemagnitude. In some embodiments, an analog signal is not an AND/ORsignal. In some embodiments, an analog signal is not a digital signal.In some embodiments, an analog signal is not a binary signal. As usedherein, a “digital signal” is a binary signal which is measured as onlypresent or absent.

In some embodiments, the cooperative input signal comprises at least twocooperative inputs. In some embodiments, the cooperative inputs aretunable. In some embodiments, the cooperative input signal comprises atleast 2, 3, 4, 5 or 10 cooperative inputs. Each possibility represents aseparate embodiment of the invention. In some embodiments, thecooperativity of the at least two inputs is tunable. As used herein, thetern “tunable” refers to the ability to be changed or modified. As theinput to the circuit is analog it has a variable value, as such theinputs which correspond to the analog input are also variable.

As used herein, the term “cooperativity” refers to manner in which twoor more molecules interact with each other and effect their ability tofunction. In some embodiments, the cooperativity is cooperativity insignaling. In some embodiments, the cooperativity is cooperativity inbinding. In some embodiments, the cooperativity is cooperativity inbinding to a promoter. In some embodiments, the cooperativity iscooperativity of at least two binding sites. In some embodiments, thecooperativity is cooperativity of at least two proteins. In someembodiments, the cooperativity is cooperativity of at least twopromoters. In some embodiments, the cooperativity is tunable. Bymutating or altering one of the cooperative molecules the cooperativitycan be changed. In some embodiments, altering the binding site tunescooperativity. In some embodiments, altering the promoter tunescooperativity. In some embodiments, alteration of a nucleic acidcomprises mutation of the nucleic acid. In some embodiments, themutation is a site directed mutagenesis to a particular mutation. Insome embodiments, the mutation is a random mutation.

As used herein, the term “operably linked” means that the nucleic acidsequence of interest is linked to the regulatory element(s), e.g. thepromoter, in a manner that allows for expression of the nucleotidesequence. In some embodiments, the promoter is linked by an interveningnucleotide sequence. In some embodiments, the promoter is linkeddirectly to the output nucleic acid sequence. In some embodiments, theoutput nucleic acid sequence is linked in frame such that the outputsequence is translated.

As used herein, the term “responsive to” refers to the promoter'sactivation status being altered by the cooperative input signal. In someembodiments, the response is to start transcription. In someembodiments, the response is to increase transcription. In someembodiments, the response is to stop transcription. In some embodiments,the response is to decrease transcription. In some embodiments, theresponse is to block transcription. In some embodiments, the response isany one of: starting, stopping, increasing, decreasing and blockingtranscription. In some embodiments, the promoter is responsive to a partof the cooperative input signal. In some embodiments, the promoter isresponsive to a part of the cooperative input signal that regulatestranscription. In some embodiments, the cooperative input signalregulates transcription and translation.

In some embodiments, the nucleic acid molecules of the invention are invectors. In some embodiments, the vectors are expression vectors orrecombinant expression vectors. Recombinant expression vectors cancomprise the circuit of the invention in a form suitable for expressionof the nucleic acids in a host cell or expression system, which meansthat the recombinant expression vectors include one or more regulatoryelements, which may be selected on the basis of the host cells to beused for expression, that is operatively-linked to the nucleic acidsequence to be expressed.

A vector nucleic acid sequence generally contains at least an origin ofreplication for propagation in a cell and optionally additionalelements, such as a heterologous polynucleotide sequence, expressioncontrol element (e.g., a promoter, enhancer), selectable marker (e.g.,antibiotic resistance), poly-Adenine sequence.

The vector may be a DNA plasmid delivered via non-viral methods or viaviral methods. The viral vector may be a retroviral vector, aherpesviral vector, an adenoviral vector, an adeno-associated viralvector or a poxviral vector. The promoters may be active in mammaliancells. The promoters may be a viral promoter.

In some embodiments, the vector is introduced into the cell by standardmethods including electroporation (e.g., as described in From et al.,Proc. Natl. Acad. Sci. USA 82, 5824 (1985)), heat shock, infection byviral vectors, high velocity ballistic penetration by small particleswith the nucleic acid either within the matrix of small beads orparticles, or on the surface, and/or the like.

General methods in molecular and cellular biochemistry, such as may beuseful for carrying out DNA and protein recombination, as well as othertechniques described herein, can be found in such standard textbooks asMolecular Cloning: A Laboratory Manual, 3rd Ed. (Sambrook et al., HaRBorLaboratory Press 2001); Short Protocols in Molecular Biology, 4th Ed.(Ausubel et al. eds., John Wiley & Sons 1999); Protein Methods (Bollaget al., John Wiley & Sons 1996); Nonviral Vectors for Gene Therapy(Wagner et al. eds., Academic Press 1999); Viral Vectors (Kaplift &Loewy eds., Academic Press 1995); Immunology Methods Manual (I.Lefkovits ed., Academic Press 1997); and Cell and Tissue Culture:Laboratory Procedures in Biotechnology (Doyle & Griffiths, John Wiley &Sons 1998).

In some embodiments, the analog signal processing circuit of theinvention further comprises a cell. In some embodiments, the analogsignal processing circuit of the invention is enclosed within a cell. Insome embodiments, the analog signal processing circuit of the inventionis in a cell. In some embodiments, the cell is a prokaryotic cell. Insome embodiments, the cell is a eukaryotic cell. In some embodiments,the cell is a prokaryotic or a eukaryotic cell. In some embodiments, thecell is an E. coli cell. In some embodiments, the eukaryotic cell is amammalian cell.

In some embodiments, the first promoter is a hybrid promoter. As usedherein, a “hybrid promoter” refers to a synthetic promoter comprising atleast two distinct elements from other promoters. In some embodiments,the promoter comprises other elements required for transcription besidesthe hybrid elements. In some embodiments, the hybrid promoter comprisesat least two regulator binding sites. As used herein, “regulators” referto molecules that regulate or modulate transcription. In someembodiments, the hybrid promoter comprises at least two protein bindingsites. In some embodiments, the hybrid promoter comprises binding sitesfor at least two proteins. In some embodiments, the proteins aretranscriptional regulators. In some embodiments, the proteins aretranscription factors. In some embodiments, the regulators are nucleicacid molecules. In some embodiments, a regulator is a transcriptionalactivator. In some embodiments, a regulator is a transcriptionalrepressor. In some embodiments, the hybrid promoter comprises a bindingsite for an activator and a binding site for a repressor. In someembodiments, at least one of the at least two regulator binding sitesbinds an activator. In some embodiments, at least one of the at leasttwo regulator binding sites binds a repressor.

In some embodiments, the at least two inputs are the regulators. In someembodiments, the at least two inputs bind to molecules that are theregulators. In some embodiments, the at least two inputs bind to the atleast two regulator binding sites. In some embodiments, the at least twoinputs bind to at least two regulators that bind to the at least tworegulator binding sites. In some embodiments, binding of an input to aregulator alters the binding affinity of the regulator to the bindingsite. In some embodiments, an input increases binding affinity. In someembodiments, an input decreases binding affinity. In some embodiments,at least one input increases binding affinity and at least one inputdecreases binding affinity.

In some embodiments, the at least two regulator binding sites are a LuxRbinding site and a LacI binding site. In some embodiments, a regulatorbinding site is a LuxR binding site. In some embodiments, a regulatorbinding site is a LacI binding site. In some embodiments, a regulatorbinding site is a riboswitch. In some embodiments, the regulators areLuxR and LacI. In some embodiments, a regulator is LuxR. In someembodiments, a regulator is LacI. In some embodiments, a regulator istheophylline. In some embodiments, the regulators are LuxR andtheophylline. In some embodiments, a regulator comprises a destabilizingmoiety. Such a moiety would result in degradation or clearance of theregulator. In some embodiments, binding of an input to the regulatorstabilizes the destabilized molecule. In some embodiments, thedestabilizing moiety is a ssrA degradation tag. In some embodiments, theat least two inputs are acyl-homoserine lactone (AHL) and isopropylβ-d-thiogalactopyranoside (IPTG). In some embodiments, an input is AHL.In some embodiments, an input is IPTG. In some embodiments, an input istheophylline. In some embodiments, the at least two inputs are AHL andtheophylline.

In some embodiments, the analog signal processing circuit furthercomprises a second promoter operably linked to a nucleic acid sequenceencoding at least one of the cooperative inputs. In some embodiments,the second promoter comprises a binding site for the at least onecooperative input. In some embodiments, the second promoter molecule isa positive feedback molecule. In some embodiments, the analog signalprocessing circuit further comprises a negative feedback molecule. Thepositive and negative feedback molecules allow for tuning of the amountof the input molecules. In this way the analog signal can be modulatedto a very wide dynamic range such as is described herein.

In some embodiments, the binding site in the second promoter comprises amodification that alters a binding affinity of the at least onecooperative input to the binding site. In some embodiments, the alteringof the binding affinity is relative to a binding affinity of the atleast one cooperative input to an unmodified binding site, or the thatbinding site before modification. Mutation of this binding site on thefeedback molecule allows for tuning of the feedback and thus tuning ofthe inputs. In some embodiments, a binding affinity to the secondpromoter of one of the at least two inputs is tunable.

In some embodiments, a binding affinity to the first promoter of atleast one of the at least two inputs is tunable. In some embodiments, abinding affinity to the first promoter of the at least two inputs istunable. In some embodiments, a binding affinity to the first promoterof at least one of the at least two regulators is tunable. In someembodiments, a binding affinity to the first promoter of the at leasttwo regulators is tunable. In some embodiments, a binding affinity tothe first promoter of at least one of the at least two regulators boundto an input in tunable. In some embodiments, a binding affinity to thefirst promoter of the at least two regulators bound to the inputs istunable.

In some embodiments, the analog signal processing circuit furthercomprises a third promoter operably linked to a nucleic acid sequenceencoding a second output molecule. In some embodiments, the thirdpromoter is responsive to the first output molecule. In someembodiments, the output molecule is a molecule for detection. In someembodiments, the output molecule is a fluorescent molecule. Fluorescentmolecules are well known in the art and include, but are not limited to,green fluorescent protein (GFP), mCherry, YFP, Cy3, Cy5, and Cy7. Insome embodiments, the first output molecule is not a molecule fordetection. In some embodiments the first output molecule is araCprotein. In some embodiments, the first output molecule is not fordetection and the second output molecule is for detection. In someembodiments, both output molecules are for detection. In someembodiments, the third promoter comprises a binding site for the firstoutput molecule. In some embodiments the first output molecule is araCprotein. In some embodiments, the third promoter comprises a pBAD site.In some embodiments, the third promoter is a pBAD promoter.

In some embodiments, the analog signal processing circuit furthercomprises arabinose. In some embodiments, the analog signal processingcircuit further comprises the inputs. In some embodiments, the analogsignal processing circuit further comprises at least one input. In someembodiments, the analog signal processing circuit further comprises atleast two inputs. In some embodiments, the analog signal processingcircuit further comprises AHL. In some embodiments, the analog signalprocessing circuit further comprises IPTG. In some embodiments, theanalog signal processing circuit further comprises theophylline. In someembodiments, the analog signal processing circuit further comprises AHLand IPTG. In some embodiments, the analog signal processing circuitfurther comprises AHL and theophylline.

In some embodiments, the analog processing circuit further comprises aregulator sequence that regulates translation of the first outputmolecule and is located between the first promoter and the nucleic acidsequence encoding for the first output molecule. In some embodiments,the analog signal processing circuit further comprises a regulatorysequence that regulates translation of the second output molecule and islocated between the third promoter and the nucleic acid sequenceencoding the second output molecule. In some embodiments, the analogsignal processing circuit further comprises (a) a regulator sequencethat regulates translation of the first output molecule and is locatedbetween the first promoter and the nucleic acid sequence encoding forthe first output molecule; (b) a regulatory sequence that regulatestranslation of the second output molecule and is located between thethird promoter and the nucleic acid sequence encoding the second outputmolecule; or (a) and (b). In some embodiments, the regulatory sequenceis part of the promoter. In some embodiments, the regulatory sequence isseparate from the promoter. In some embodiments, the regulatory sequenceis in the nucleic acid sequence encoding the output molecule. In someembodiments, the regulatory sequence is not in the nucleic acid sequenceencoding the output molecule. In some embodiments, the regulatorysequence is in a non-coding region. the output molecule. In someembodiments, the regulatory sequence is in a non-coding region after thenucleic acid sequence encoding the output molecule. In some embodiments,the regulatory sequence is in a non-coding region before the nucleicacid sequence encoding the output molecule. In some embodiments, theregulatory sequence is in a non-coding region before or after thenucleic acid sequence encoding the output molecule. In some embodiments,the regulatory sequence is in an untranslated region (UTR). In someembodiments, the regulatory sequence is in the 3′ UTR. In someembodiments, the regulatory sequence is in the 5′ UTR.

In some embodiments, the regulatory sequence is a regulatory RNA bindingsite. In some embodiments, the regulatory sequence is a miR bindingsite. In some embodiments, the regulatory sequence is a siRNA bindingsite. In some embodiments, the regulatory sequence is a lncRNA bindingsite. In some embodiments, the input is the regulatory RNA. In someembodiments, the input is the miR. In some embodiments, the input is thesiRNA. In some embodiments, the input is the lncRNA.

In some embodiments, the regulatory sequence is a riboswitch. In someembodiments, the regulatory sequence codes for a riboswitch in thetranslated mRNA. As used herein, the term “riboswitch” refers to asegment in an mRNA that binds to specific effector molecules andmodifies the riboswitch-containing mRNA's protein production. In someembodiments, the riboswitch modified at least one of mRNA stability,translation rate, and translational elongation. In some embodiments, theriboswitch modifies translation rate. In some embodiments, binding ofthe effector molecule decreases or halts translation. In someembodiments, binding of the effector molecule increases or startstranslation. It will be understood by one skilled in the art that theeffector molecule is one of the cooperative inputs, specifically aninput that regulates translation of the output molecule. In someembodiments, the effector molecule is a small molecule. In someembodiments, the effector molecule is a metabolite. In some embodiments,the effector molecule is theophylline. In some embodiments, the effectormolecule is a cooperative input.

In some embodiments, the first promoter is responsive to a proteincomprising more than one subunit. In some embodiments, the firstpromoter is responsive to a protein complex comprising more than onesubunit. In some embodiments, the protein or protein complex consists ofmore than one subunit. In some embodiments, the protein or proteincomplex consists of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12 subunits. Eachpossibility represents a separate embodiment of the invention. In someembodiments, the at least two cooperative inputs are at least two of thesubunits. In some embodiments, the at least two cooperative inputs areall of the subunits of the protein or complex. In some embodiments, theat least two cooperative inputs are all of the subunits of the proteinor complex required to regulate the promoter. In some embodiments, thecooperativity of the subunits is determined by the binding affinities ofthe subunits. In some embodiments, the cooperativity of the subunits isdetermined by the expression levels of the subunits.

In some embodiments, the protein consisting of more than one subunit isa transcription factor. In some embodiments, the protein consisting ofmore than one subunit is a polymerase. In some embodiments, the proteinconsisting of more than one subunit is a nuclease. In some embodiments,the nuclease is an endonuclease. In some embodiments, the polymerase isan RNA polymerase.

In some embodiments, the RNA polymerase is T7 RNA polymerase. In someembodiments, the at least two cooperative inputs are T7 RNA polymerasesubunits. In some embodiments, the T7 RNA polymerase subunits areselected from an alpha-fragment subunit of T7 RNA polymerase, asigma-fragment subunit of T7 RNA polymerase and a beta-core fragmentsubunit of T7 RNA polymerase. In some embodiments, the at least twoinputs are an alpha-fragment subunit of T7 RNA polymerase, asigma-fragment subunit of T7 RNA polymerase and a beta-core fragmentsubunit of T7 RNA polymerase. In some embodiments, the endonuclease isCas9.

In some embodiments, the analog signal processing circuit of theinvention further comprises a nucleic acid sequence coding for at leastone of the subunits. In some embodiments, the analog signal processingcircuit of the invention comprises a nucleic acid sequence coding forall the subunits. In some embodiments, the nucleic acid sequences codingfor the subunits are operably linked to at least one promoter. In someembodiments, all the subunit-encoding nucleic acid sequences areoperably linked to the same promoter. In some embodiments, all thesubunit-encoding nucleic acid sequences are not operably linked to thesame promoter. In some embodiments, all the subunit-encoding nucleicacid sequences are operably linked to different promoters. In someembodiments, the subunit-encoding nucleic acid sequences are operablylinked to a plurality of promoters. In some embodiments, eachsubunit-encoding nucleic acid sequence is linked to one promoter. Insome embodiments, each subunit-encoding nucleic acid sequence is linkedto only one promoter, and at least two promoters are so linked. Askilled artisan will understand that each sequence can be linked to morethan one promoter or to several promoters. Similarly, more than onesequence can be linked to a single promoter (thus having coordinatedexpression) or each sequence can have its own separate promoter(uncoordinated expression). Lastly, some of the sequences coding forsubunits may be operably linked to the same promoter (coordinatedexpression), while others may have separate promoters (uncoordinated).

In some embodiments, the cooperativity of the inputs is determined bythe binding affinities of the promoters. In some embodiments, thepromoters are not constitutively active, and the cooperativity of theinputs is determined by the binding affinities of the promoters for anactivating molecule. In some embodiments, at least one of thecooperative inputs is an activating molecule for a promoter operablylinked to a nucleic acid sequence encoding a subunit. In someembodiments, the inputs are the activating molecules. In someembodiments, the inputs are the subunits and the activating moleculesare used to tune the inputs. In some embodiments, the inputs are thesubunits and the activating molecules are used to tune the cooperativityof the inputs.

In some embodiments, the at least two cooperative inputs are an enzymeand at least one of the enzyme's cofactors. As used herein, a “cofactor”refers to a molecule, other than the substrate, whose presence isessential for the activity of the enzyme. In some embodiments, theenzyme acts on the promoter. In some embodiments, the enzyme acts on anucleic acid molecule comprising the promoter. In some embodiments, theenzyme is selected from a polymerase, a helicase, a nuclease, arecombinase and a transferase. In some embodiments, the cooperativity ofthe enzyme and cofactor is determined by the binding affinities to eachother. In some embodiments, the cooperativity of the enzyme and cofactoris determined by the expression levels of the enzyme and cofactor. Insome embodiments, tuning the cooperativity comprises mutating the enzymeor cofactor, or the interaction sites of the enzyme and cofactor.

In some embodiments, the enzyme is Cas9. In some embodiments, thecofactor is a small guide RNA (sgRNA). In some embodiments, thetunability of the Cas9 and sgRNA is determined by mutating the sgRNAsequence. In some embodiments, the tunability of the Cas9 and sgRNA isdetermined by altering a binding affinity of the Cas9 to the sgRNA. Insome embodiments, mutating the sgRNA sequence alters the bindingaffinity of the Cas9 to the sgRNA.

According to some embodiments, Cas9, unwinds DNA duplex and searches forsequences matching the sgRNA to cleave. Target recognition occurs upondetection of complementarity between a “protospacer” sequence in thetarget DNA and the remaining spacer sequence in the sgRNA. Importantly,Cas9 cuts the DNA only if a correct protospacer-adjacent motif (PAM) isalso present at the 3′ end. According to certain embodiments, differentprotospacer-adjacent motif can be utilized. For example, the S. pyogenessystem requires an NGG sequence, where N can be any nucleotide.Bioinformatic analyses have generated extensive databases of CRISPR lociin a variety of bacteria that may serve to identify additional usefulPAMs and expand the set of CRISPR-targetable. In S. pyogenes, Cas9generates a blunt-ended double-stranded break 3 bp upstream of theprotospacer-adjacent motif (PAM) via a process mediated by two catalyticdomains in the protein: an HNH domain that cleaves the complementarystrand of the DNA and a RuvC-like domain that cleaves thenon-complementary strand.

The term “single guide RNA” (sgRNA), is a 20 bp RNA molecule that canform a complex with Cas9 and serve as the DNA recognition module. sgRNAis typically designed as a synthetic fusion of the CRISPR RNA (crRNA)and the trans-activating crRNA.

Cas9 proteins are known to exist in many Type II CRISPR systemsincluding, but not limited to the following: Methanococcus maripaludisC7; Corynebacterium diphtheriae; Corynebacterium efficiens YS-314;Corynebacterium glutamicum ATCC 13032 Kitasato; Corynebacteriumglutamicum ATCC 13032 Bielefeld; Corynebacterium glutamicum R;Corynebacterium kroppenstedtii DSM 44385; Mycobacterium abscessus ATCC19977; Nocardia farcinica IFM10152; Rhodococcus erythropolis PR4;Rhodococcus jostii RHA1; Rhodococcus opacus B4 uid36573; Acidothermuscellulolyticus 11B; Arthrobacter chlorophenolicus A6; Kribbella flavidaDSM 17836 uid43465; Thermomonospora curvata DSM 43183; Bifidobacteriumdentium Bdl; Bifidobacterium longum DJO10A; Slackia heliotrinireducensDSM 20476; Persephonella marina EX HI; Bacteroides fragilis NCTC 9434;Capnocytophaga ochracea DSM 7271; Flavobacterium psychrophilum JIP02 86;Akkermansia muciniphila ATCC BAA 835; Roseiflexus castenholzii DSM13941; Roseiflexus RSI; Synechocystis PCC6803; Elusimicrobium minutumPeil91; uncultured Termite group 1 bacterium phylotype Rs D17;Fibrobacter succinogenes S85; Bacillus cereus ATCC 10987; Listeriainnocua; Lactobacillus casei; Lactobacillus rhamnosus GG; Lactobacillussalivarius UCC1 18; Streptococcus agalactiae A909; Streptococcusagalactiae NEM316; Streptococcus agalactiae 2603; Streptococcusdysgalactiae equisimilis GGS 124; Streptococcus equi zooepidemicus MGCS10565; Streptococcus gallolyticus UCN34 uid46061; Streptococcus gordoniiChallis subst CHI; Streptococcus mutans NN2025 uid46353; Streptococcusmutans; Streptococcus pyogenes Ml GAS; Streptococcus pyogenes MGAS5005;Streptococcus pyogenes MGAS2096; Streptococcus pyogenes MGAS9429;Streptococcus pyogenes MGAS 10270; Streptococcus pyogenes MGAS6180;Streptococcus pyogenes MGAS315; Streptococcus pyogenes SSI-1;Streptococcus pyogenes MGAS 10750; Streptococcus pyogenes NZ131;Streptococcus thermophiles CNRZ1066; Streptococcus thermophiles LMD-9;Streptococcus thermophiles LMG 18311; Clostridium botulinum A3 LochMaree; Clostridium botulinum B Eklund 17B; Clostridium botulinum Ba4657;Clostridium botulinum F Langeland; Clostridium cellulolyticum H10;Finegoldia magna ATCC 29328; Eubacterium rectale ATCC 33656; Mycoplasmagallisepticum; Mycoplasma mobile 163K; Mycoplasma penetrans; Mycoplasmasynoviae 53; Streptobacillus moniliformis DSM 12112; BradyrhizobiumBTAil; Nitrobacter hamburgensis X14; Rhodopseudomonas palustris BisB18;Rhodopseudomonas palustris BisB5; Parvibaculum lavamentivorans DS-1;Dinoroseobacter shibae DFL 12; Gluconacetobacter diazotrophicus Pal5FAPERJ; Gluconacetobacter diazotrophicus Pal 5 JGI; Azospirillum B510uid46085; Rhodospirillum rubrum ATCC 11170; Diaphorobacter TPSYuid29975; Verminephrobacter eiseniae EF01-2; Neisseria meningitides053442; Neisseria meningitides alphal4; Neisseria meningitides Z2491;Desulfovibrio salexigens DSM 2638; Campylobacter jejuni doylei 26997;Campylobacter jejuni 81116; Campylobacter jejuni; Campylobacter lariRM2100; Helicobacter hepaticus; Wolinella succinogenes; Tolumonasauensis DSM 9187; Pseudoalteromonas atlantica T6c; Shewanella pealeanaATCC 700345; Legionella pneumophila Paris; Actinobacillus succinogenes130Z; Pasteurella multocida; Francisella tularensis novicida U112;Francisella tularensis holarctica; Francisella tularensis FSC 198;Francisella tularensis tularensis; Francisella tularensis WY96-3418; andTreponema denticola ATCC 35405.

One skilled in the art will appreciate that any Cas9 known in the artmay be utilized in the circuits and methods described herein. Anymutations or modifications to Cas9 such as are known in the art may alsobe used. Similarly, any sgRNA such as can be designed and will target apromoter of the invention may be used. There are a number of publiclyavailable tools available to help choose and/or design target sequencesas well as lists of bioinformatically determined unique gRNAs fordifferent genes in different species, including but not limited to theTarget Finder, (e.g., E-CRISP), the RGEN Tools: Cas-OFFinder, theCasFinder: Flexible algorithm for identifying specific Cas9 targets ingenomes and the CRISPR Optimal Target Finder.

In some embodiments, the analog signal processing circuit furthercomprises a nucleic acid sequences encoding at least one of the inputs.In some embodiments, the nucleic acid sequences encoding the input isoperably linked to a promoter. In some the input is tuned by adding amolecule that binds to the promoter and modulates translation. In someembodiments, the promoter is not constitutively active. In someembodiments, the expression of an input is tuned by the binding affinityof the promoter to the molecule that modulates translation. In someembodiments, the expression of the input is tuned by mutating ormodifying the binding site for the molecule that modulates translation.

In some embodiments, the at least two cooperative inputs are at leasttwo factors that share a common binding site. In some embodiments, thefirst promoter comprises the common binding site. In some embodiments,the at least two cooperative inputs compete for the common binding site.In some embodiments, the inputs are different molecules that share thesame binding site. In some embodiments, the inputs bind differentbinding sites that overlap in the first promoter. In some embodiments,the two factors only bind to the binding site when both factors areexpressed. In some embodiments, the factors modulate transcription. Insome embodiments, the factors are transcription factors. In someembodiments, at least one factor modulates transcription. In someembodiments, the analog signal processing circuit further comprises theat least two factors that share a common binding site. In someembodiments, the at least two factors that share a common binding siteare a Sigma factor and an anti-Sigma factor. DNA binding proteins withthe same or overlapping binding sites are well known in the art, and anysuch factors where at least one would modulate transcription from thepromoter may be used.

In some embodiments, the first promoter operably further comprises afourth promoter that transcribes in a direction opposite to thetranscriptional direction of the first promoter. Nested promoters arewell known in the art. Such promoters can translate in the samedirection or in opposite directions. Thus, two promoters can exist inthe same sequence, but transcribe in opposite directions. Such oppositetranscription causes interference between the two promoters as theycompete to transcribe. In some embodiments, at least one input binds toactive the first promoter and at least one input binds to active thefourth promoter. In some embodiments, binding of at least one of the atleast two inputs to the fourth promoter interferes with transcriptionfrom the first promoter.

In some embodiments, the present invention provides an analog signalprocessing circuit comprising:

-   -   a. a first tunable promoter operably linked to a nucleic acid        sequence coding for a DNA recombinase;    -   b. a second constitutive promoter operably linked to a nucleic        acid sequence that when inverted codes for a first output        molecule and wherein the nucleic acid sequence is flanked by        recognition sites for the DNA recombinase; and    -   c. decoy recognition sites for the DNA recombinase.

In some embodiments, the recombinase is a unidirectional recombinase. Insome embodiments, the recombinase is a serine recombinase. In someembodiments, the recombinase is a PhiC31 recombinase. In someembodiments, the recombinase is non-reversible. In some embodiments, therecognition sites are identical. In some embodiments, the recognitionsites are not identical. In some embodiments, the recognition sites nolonger function if inverted. In some embodiments, the decoy recognitionsites are inverses of the recognition sites. The location of the decoysites may be anywhere in the system. In some embodiments, the decoysites are within a nucleic acid molecule comprising the first tunablepromoter. In some embodiments, the decoy sites are within a nucleic acidmolecule comprising the second constitutive promoter. In someembodiments, the decoy sites are within a third nucleic acid molecule.In some embodiments, the decoy sites are within: (i) a nucleic acidmolecule comprising (a), (ii) a nucleic acid molecule comprising (b), or(iii) a third nucleic acid molecule.

In some embodiments, the constitutive promoter produces no, or very lowlevels, of the output molecule. In some embodiments, the nucleic acidsequence comprising the output molecule further comprises an insulatorcomponent that reduces expression of the inverted output molecule, butnot expression of the correctly oriented output. In some embodiments,the insulator is a ribozyme-based insulator. In some embodiments, theinsulator is RiboJ. In some embodiments, the insulator is in the UTR ofthe output sequence. In some embodiments, the insulator is in the 5′ UTRof the output sequence.

In some embodiments, the tunable promoter comprises a regulator bindingsite. In some embodiments, the regulator binding site is a Plux bindingsite, and the promoter is tunable by addition of AHL, Plux or both.

In some embodiments, in order to ensure low basal transcription fromtunable promoters, the protein produced by the promoter comprises adegradation tag. In some embodiments, the degradation tag is a ssrAdegradation tag. Such a tag may be used with any of the tunablepromoters of the invention.

In some embodiments, the contacting comprises adding an input. In someembodiments, the contacting comprises expressing an input in the cell orcircuit. In some embodiments, expressing an input comprises contactingthe cell or circuit with a protein that binds to a promoter thantranscribes an input. In some embodiments, the contacting comprisestransfecting an input into the cell. In some embodiments, the contactingcomprises contacting the cell or circuit with a protein that binds aninput. In some embodiments, the contacting comprises contacting the cellor circuit with a protein that binds a promoter and inducestranscription of an input. In some embodiments, the contacting comprisescontacting the cell or circuit with at least one vector comprising anucleic acid molecule of the invention. In some embodiments, at leastone of the nucleic acid sequences of the invention are in a vector. Insome embodiments, the nucleic acid sequences are in one vector. In someembodiments, the nucleic acid sequences are in a plurality of vectors.In some embodiments, the invention provides at least one vectorcomprising the nucleic acid molecules of the invention. In someembodiments, a circuit of the invention comprises at least one vectorcomprising the nucleic acid sequences of the invention.

Expressing of a gene within a cell is well known to one skilled in theart. It can be carried out by, among many methods, transfection, viralinfection, or direct alteration of the cell's genome. In someembodiments, the gene is in an expression vector such as plasmid orviral vector. One such example of an expression vector containingp16-Ink4a is the mammalian expression vector pCMV p16 INK4A availablefrom Addgene.

A vector nucleic acid sequence generally contains at least an origin ofreplication for propagation in a cell and optionally additionalelements, such as a heterologous polynucleotide sequence, expressioncontrol element (e.g., a promoter, enhancer), selectable marker (e.g.,antibiotic resistance), poly-Adenine sequence.

The vector may be a DNA plasmid delivered via non-viral methods or viaviral methods. The viral vector may be a retroviral vector, aherpesviral vector, an adenoviral vector, an adeno-associated viralvector or a poxviral vector. The promoters may be active in mammaliancells. The promoters may be a viral promoter.

In some embodiments, the gene is operably linked to a promoter. The term“operably linked” is intended to mean that the nucleotide sequence ofinterest is linked to the regulatory element or elements in a mannerthat allows for expression of the nucleotide sequence (e.g. in an invitro transcription/translation system or in a host cell when the vectoris introduced into the host cell).

In some embodiments, the vector is introduced into the cell by standardmethods including electroporation (e.g., as described in From et al.,Proc. Natl. Acad. Sci. USA 82, 5824 (1985)), Heat shock, infection byviral vectors, high velocity ballistic penetration by small particleswith the nucleic acid either within the matrix of small beads orparticles, or on the surface (Klein et al., Nature 327. 70-73 (1987)),and/or the like.

The term “promoter” as used herein refers to a group of transcriptionalcontrol modules that are clustered around the initiation site for an RNApolymerase i.e., RNA polymerase II. Promoters are composed of discretefunctional modules, each consisting of approximately 7-20 bp of DNA, andcontaining one or more recognition sites for transcriptional activatoror repressor proteins.

In some embodiments, nucleic acid sequences are transcribed by RNApolymerase II (RNAP II and Pol II). RNAP II is an enzyme found ineukaryotic cells. It catalyzes the transcription of DNA to synthesizeprecursors of mRNA and most snRNA and microRNA.

In some embodiments, mammalian expression vectors include, but are notlimited to, pcDNA3, pcDNA3.1 (±), pGL3, pZeoSV2(±), pSecTag2, pDisplay,pEF/myc/cyto, pCMV/myc/cyto, pCR3.1, pSinRep5, DH26S, DHBB, pNMT1,pNMT41, pNMT81, which are available from Invitrogen, pCI which isavailable from Promega, pMbac, pPbac, pBK-RSV and pBK-CMV which areavailable from Strategene, pTRES which is available from Clontech, andtheir derivatives.

In some embodiments, expression vectors containing regulatory elementsfrom eukaryotic viruses such as retroviruses are used by the presentinvention. SV40 vectors include pSVT7 and pMT2. In some embodiments,vectors derived from bovine papilloma virus include pBV-1MTHA, andvectors derived from Epstein Bar virus include pHEBO, and p205. Otherexemplary vectors include pMSG, pAV009/A+, pMTO10/A+, pMAMneo-5,baculovirus pDSVE, and any other vector allowing expression of proteinsunder the direction of the SV-40 early promoter, SV-40 later promoter,metallothionein promoter, murine mammary tumor virus promoter, Roussarcoma virus promoter, polyhedrin promoter, or other promoters showneffective for expression in eukaryotic cells.

In some embodiments, recombinant viral vectors, which offer advantagessuch as lateral infection and targeting specificity, are used for invivo expression. In one embodiment, lateral infection is inherent in thelife cycle of, for example, retrovirus and is the process by which asingle infected cell produces many progeny virions that bud off andinfect neighboring cells. In one embodiment, the result is that a largearea becomes rapidly infected, most of which was not initially infectedby the original viral particles. In one embodiment, viral vectors areproduced that are unable to spread laterally. In one embodiment, thischaracteristic can be useful if the desired purpose is to introduce aspecified gene into only a localized number of targeted cells.

Various methods can be used to introduce the expression vector of thepresent invention into cells. Such methods are generally described inSambrook et al., Molecular Cloning: A Laboratory Manual, Cold SpringsHarbor Laboratory, New York (1989, 1992), in Ausubel et al., CurrentProtocols in Molecular Biology, John Wiley and Sons, Baltimore, Md.(1989), Chang et al., Somatic Gene Therapy, CRC Press, Ann Arbor, Mich.(1995), Vega et al., Gene Targeting, CRC Press, Ann Arbor Mich. (1995),Vectors: A Survey of Molecular Cloning Vectors and Their Uses,Butterworths, Boston Mass. (1988) and Gilboa et at. [Biotechniques 4(6): 504-512, 1986] and include, for example, stable or transienttransfection, lipofection, electroporation and infection withrecombinant viral vectors. In addition, see U.S. Pat. Nos. 5,464,764 and5,487,992 for positive-negative selection methods.

In one embodiment, plant expression vectors are used. In one embodiment,the expression of a polypeptide coding sequence is driven by a number ofpromoters. In some embodiments, viral promoters such as the 35S RNA and19S RNA promoters of CaMV [Brisson et al., Nature 310:511-514 (1984)],or the coat protein promoter to TMV [Takamatsu et al., EMBO J. 6:307-311(1987)] are used. In another embodiment, plant promoters are used suchas, for example, the small subunit of RUBISCO [Coruzzi et al., EMBO J.3:1671-1680 (1984); and Brogli et al., Science 224:838-843 (1984)] orheat shock promoters, e.g., soybean hsp17.5-E or hsp17.3-B [Gurley etal., Mol. Cell. Biol. 6:559-565 (1986)]. In one embodiment, constructsare introduced into plant cells using Ti plasmid, Ri plasmid, plantviral vectors, direct DNA transformation, microinjection,electroporation and other techniques well known to the skilled artisan.See, for example, Weissbach & Weissbach [Methods for Plant MolecularBiology, Academic Press, NY, Section VIII, pp 421-463 (1988)]. Otherexpression systems such as insects and mammalian host cell systems,which are well known in the art, can also be used by the presentinvention.

It will be appreciated that other than containing the necessary elementsfor the transcription and translation of the inserted coding sequence(encoding the polypeptide), the expression construct of the presentinvention can also include sequences engineered to optimize stability,production, purification, yield or activity of the expressedpolypeptide.

A person with skill in the art will appreciate that a gene can also beexpressed from a nucleic acid construct administered to the individualemploying any suitable mode of administration, described hereinabove(i.e., in vivo gene therapy). In one embodiment, the nucleic acidconstruct is introduced into a suitable cell via an appropriate genedelivery vehicle/method (transfection, transduction, homologousrecombination, etc.) and an expression system as needed and then themodified cells are expanded in culture and returned to the individual(i.e., ex vivo gene therapy).

In some embodiments, the detecting comprises quantification of theoutput molecule. In some embodiments, the quantification comprisesmeasuring the fluorescence of the output molecule. Methods of proteinquantification are well known in the art, and include but are notlimited to immunoblotting, ELISA, FACS to name but a few.

In some embodiments, the digital output is either a positive or anegative output. In some embodiments, the output is ether present orabsent. In some embodiments, the method further comprises tuning athreshold for converting the analog input into a positive digitaloutput. This threshold is the value at which the digital output ispresent. In some embodiments, the tuning comprises tuning expression ofat least one of the at least two regulators. In some embodiments, thetuning comprises tuning a binding efficiency of at least one of the atleast two inputs to a binding site. In some embodiments, the tuningcomprises tuning a binding efficiency of at least one of the at leasttwo regulators to a binding site. In some embodiments, the tuningcomprises adding a molecule that binds to the regulatory sequence. Insome embodiments, the tuning comprises adding a molecule that binds tothe first output molecule and alters binding of the first outputmolecule to the third promoter. In some embodiments, the tuningcomprises at least one of (a) tuning expression of at least one of saidat least two regulators; (b) tuning a binding efficiency of at least oneof said at least two inputs to a binding site; (c) tuning a bindingefficiency of at least one of said at least two regulators to a bindingsite; (d) adding a molecule that binds to said regulatory sequence; and(e) adding a molecule that binds to said first output molecule andalters binding of said first output molecule to said third promoter.

Mapping Neural Networks to Molecular Networks

The basic computational element in ANNs is the perceptron (FIG. 1A),which performs three operations: (i) summing all the inputs in analogfashion, (ii) multiplication of each input (x_(i)) by analog scalar(w_(i)) that represents the synaptic (strength) weight, and (3) anon-linear neural activation (thresholding). The correspondingperceptron's output is given by:

$\begin{matrix}{z = \left\{ \begin{matrix}{{}_{}^{}{}_{}^{}} & {{{\sum_{i}{w_{i} \cdot x_{i}}} - y_{th}} \geq 0} \\{{}_{}^{}{}_{}^{}} & {otherwise}\end{matrix} \right.} & (1)\end{matrix}$

In equation (1), a shifted signum (step) activation function was used.The perceptron is an abstract model that can capture the computationalpower of biological neurons. Because, as was previously shown,biological and neural architectures share many features, a novel simpletransformation between the basic computational structure of perceptronand molecular processing unit can be discerned. Accordingly, aninteraction between proteins and DNA that controls the promoter activity(P_(r)) can be viewed either as a node or as an activation functionwhich, in turn, can be simply described by a Michaelis-Menten model.Promoter is a region of DNA that initiates transcription of a particulargene. In human genetic circuits, transcription is followed bytranslation that leads to a protein synthesis. A sigmoid function can bethen used to describe the promoter activity:

$\begin{matrix}{P_{r} = {{P_{on}\frac{e^{\ln {({y/K_{d}})}}}{1 + e^{\ln {({y/K_{d}})}}}} + P_{off}}} & (2)\end{matrix}$

where, K_(d) is a dissociation constant of protein (y) binding to DNA,P_(off) is the basal level, and P_(on) is the maximum activity achievedby the system. In equation (2), a single binding site in the promoterwas assumed. The promoter activity can be simply viewed as a sigmoidfunction in a log-linear domain. As a first-order approximation, fory≥K_(d) or y≤0.1 Kd, the promoter activity asymptotically accepts twodiscrete levels (P_(on) and P_(off)). Now, it may be assumed that y isrepresented by a combinational analog function of input vector, (y is amulti-protein complex formed by other proteins that bind together). Inthis case, and in analogy to perceptron, y will be the inputs'multiplication outcome y=Π_(i)x_(i) rather than their summation outcome(y=Σ_(i)x_(i) Equation 1 when w_(i)=1). As can be gleaned from FIG. 1Bthat, to activate the log-linear sigmoid function from a low to a highlevel, the two inputs must be multiplied by each other rather summated;summing them could activate the linear-linear sigmoid function from alow to a high level (FIG. 1C). The next chronological step is to definethe strength (weight) of the inputs. While biologists have shown that“two is better than one,” little is known about the design principles ofcooperative binding, a phenomenon that occurs in biochemistry to enhanceand stabilize the biological complexity of reactions, for scaling thecomputational complexity of biological networks in living cells. Thereare three main models of cooperativity in living cells (FIG. 1D): (i)identical molecules bind to a protein that contains multiple bindingsites, (ii) protein subunits bind to form a multiprotein complex(quaternary structure); the subunits are regulated by the same openreading frame/promoter/operon, (iii) identical proteins/transcriptionfactors bind to promoters with multiple binding sites. In the threemodels, cooperativity often increases the affinity for binding of theother subunits and is modeled by a power law function (x^(n), where n isknown as the Hill coefficient, which denotes the effective number ofidentical units that interact). From an engineering perspective,cooperativity in living cells can be described as the number ofindependent components that collectively act, analogous to thecomputational role of synapses in ANNs. Thus, the strength of everyinput (weight) activated by a log-linear sigmoid will be determined bythe cooperativity, is given by:

$\begin{matrix}{z = \left\{ {{\begin{matrix}{{}_{}^{}{}_{}^{}} & {\frac{\Pi_{i}x_{i}^{n_{i}}}{y_{th}} > 1} \\{{}_{}^{}{}_{}^{}} & {otherwise}\end{matrix}{or}z} = \left\{ \begin{matrix}{{}_{}^{}{}_{}^{}} & {{{\sum_{i}{n_{i} \cdot {\ln \left( x_{i} \right)}}} - {\ln \left( y_{th} \right)}} > 0} \\{{}_{}^{}{}_{}^{}} & {otherwise}\end{matrix} \right.} \right.} & (3)\end{matrix}$

In analogy to the perceptron, it was assumed that the activity of thepromoter in equation (3) is a signum function, however in natural andsynthetic systems, it is approximated as a log-linear sigmoid function(Hill-function). By this, there was developed a new model, termed‘perceptgene,’ inspired by molecular biology (FIG. 1), with powerfulcomputational abilities. Equation (3) is equivalent to equation (1)(perceptron/linear-classifier) in a log-linear domain, as illustrated inFIG. 1E. The perceptgene is inspired by molecular biology and has acomputational process identical to that of the perceptron, i.e.,consisting of three operations: (i) multiplication of all the inputs inanalog fashion (this process is mainly implemented by bindingreactions), (ii) each input (x_(i)) is invoked by a power law functionwith a coefficient n, that represents the cooperativity bindingreaction, and (iii) a log-linear activation function that is implementedby promoter activity or a bio-enzymatic reaction (thresholding). Thecorresponding binary-fashion perceptgene output depends on the thresholdaccordingly. The simulation results (FIG. 1F) of equation (3) suggestthat the perceptgene is a type of a linear classifier in a log-lineardomain and, in contrast to the perceptron, a small change in thecooperativity weight causes large separability. In summary, a perceptronis a binary classifier that makes its decision based on a linearpredictor function combining a set of weights with the input vector.Analogously, the perceptgene is a binary classifier that makes itsdecision based on a log-linear predictor function, multiplying a set ofnon-linear weights with the input vector.

Synthetic Molecular Networks (SMNs) in Living Cells

SMNs attempt to transfer principles of neural networks into biologicaldesign, to build large-scale robust-intelligent living systems. As aproof of concept, a synthetic perceptgene was constructed in livingcells, which acts as a log-linear classifier (FIG. 2A-H). As a firststep, there will be described two different systems performing amultiplication with weighted cooperativity. The systems accept AHL andIPTG chemicals as inputs and express a fluorescent protein (GFP ormcherry) as an output. The first system is implemented by a well-knownsynthetic hybrid promoter consisting of the LuxR activator and LacIrepressor. In asymptotic boundary conditions, the hybrid promoter isonly activated in the presence of LuxR and absence of LacI at thepromoter. AHL and IPTG molecules bind to LuxR and Lad, respectively, andchange their protein structure, which change protein's binding activityto the promoter. Asymptotically, at high concentrations of both AHL andIPTG, LuxR is bound and LacI is free, therefore, the promoter isactivated. This circuit is widely used in synthetic biology to implementAND logic gate. To achieve an analog multiplication rather than an ANDlogic gate, an ssrA degradation tag was added to the Lad repressor,which reduces the life-time and the copy number of LacI in steady state.Furthermore, graded positive feedback (PF) and negative feedback (NF)loops were used to regulate the expression of LuxR and Lad,respectively, thereby strikingly increasing the dynamic ranges of AHLand IPTG input. The graded PF loop was achieved by creating randommutations in the LuxR-DNA binding site sequence within the promoter,causing reduced binding efficiency of LuxR to promoter. The NF and PFloops were cloned on low copy number of plasmids (LCP) and the hybridpromoter was cloned on a medium copy number of plasmids (MCP), whichacts as a shunt. The purpose of adding a shunt is to preventoscillations of the NF loop and to broaden the dynamic ranges oftranscription factors (TFs) inputs. The experimental result of theanalog multiplier based on a hybrid promoter is presented in FIG. 2B.The effective Hill coefficients of the system is 0.5 for AHL and 0.7 forIPTG. In natural systems, two AHL molecules bind to one LuxR protein,and one complex AHL-LuxR binds to the promoter, thus, the Hillcoefficient of the LuxR system should theoretically be equal to 2,however, the inherent negative feedback in the binding reactions betweenthe LuxR and AHL (the concentration of total LuxR is constant) reducedit to lower values. Furthermore, in our systems, the mutated PF loop andhybrid promoter also reduced the Hill coefficient. A similar explanationcould be given for IPTG-LacI cooperativity. The second multiplier systemis implemented in the transcription-translation level using LuxR andRiboswitch (FIG. 2C). The system has two inputs, theophylline and AHL(FIG. 2D). Theophylline is a small molecule that interacts with theuntranslated region of mRNA (5′ UTR), and regulates the translationprocess of targeted gene expression. The Hill coefficient of such asystem is 0.5 for theophylline and 0.2 for AHL, unequal to the firstsystem. This can be explained because both systems were cloned ondifferent copy number shunt plasmids. Eventually, a perceptgene inliving cells was implemented by cascading a log-linear sigmoidactivation function to the analog multiplier. This was achieved byreplacing the output of the P_(lux/lacO) hybrid promoter with the araCgene and adding the P_(BAD) promoter that controls the output GFPprotein (FIG. 2E). An araC was used as an activator, by adding arabinoseto the cell culture. The arabinose-AraC complex binds strongly to theP_(BAD) promoter, eliciting a sharp input-output transfer response.Thus, it can act with a log-linear sigmoid behavior. FIG. 2F showsexperimental results of the perceptgene in living cells; the activationfunction that is implemented by the P_(BAD) promoter converts the analogbehavior of the multiplier to a first-order binary classifier. To betterunderstand these results, a linear domain classifier (perceptron) wassimulated by transforming perceptgene parameters (weights, threshold andscale) from log scale to linear scale. Our simulation results show thata summation in linear scale (FIG. 2G) has a similar behavior to amultiplication in log-scale (FIG. 2B), and that a perceptron (FIG. 2H)based on a sigmoid activation function, has a similar behavior to aperceptgene based on a Hill function (FIG. 2E).

An Analog Synthetic Parts Library

The experimental results of hybrid promoters and other complex proteinshave been shown in several synthetic biology works, which aimed torealize ‘AND-logic-gate’, binging researchers construct them mainly byreducing the input dynamic range of these synthetic parts. The noveltyof the present invention lies in exploiting the analog complexoperations naturally existing in living cells, e.g., binding reactionsthat mimic analog multiplication, and integrating them with digitalcomponents, to achieve very powerful computing networks (perceptgene inSMNs). As a first step, a library of analog synthetic parts was builtwith a wide input dynamic range, using feedback loops and log-linearinput-output transfer functions. The synthetic parts performance wasimproved upon by developing new methods for increasing their inputdynamic range. For example, FIG. 3A shows new graded PF circuits whichhave a very wide input dynamic range, with five orders of magnitude forAHL-LuxR and arabinose-AraC. In some embodiments, these circuits may befurther improved by more than one order of magnitude. These results werebased on an analytical model of graded PF (see, e.g., gates in singlecells. Nature. 2012; 491(7423):249-253. doi:10.1038/nature11516.

46. L R, Y R. Noise Tolerance Analysis for Reliable Analog and DigitalComputation in Living Cells. J Bioeng Biomed Sci. 2016; 6(2).doi:10.4172/2155-9538.1000186). Furthermore, well-known methods insynthetic biology were applied to either control the slope ofinput-output transfer function or to adjust the basal level of ouranalog synthetic biology parts. This method may then be generalized toother synthetic parts (e.g., T7 RNA polymerase, CRISPR, Segma Factor,LacI and others).

A Library of Analog Multipliers and Control the Cooperativity Weights

It was shown above that genetic circuits that inherently exhibit bindingreactions in living cells, can be applied to construct analogmultipliers (FIG. 2). Previously, synthetic biologists have successfullydeveloped several robust synthetic systems that demonstrate bindingreactions in living cells (bacteria, yeast and mammalian cells). Thus,these systems may be further used to build a library of analogmultipliers with programmable cooperativity weights. Three systems maybe thus used:

-   -   The T7 RNA polymerase (RNAp) system, which is widely used in        synthetic biology and has recently been successfully divided to        several fragments that have to be functionally co-expressed.        This system mainly consists of three subunits: (i) σ-fragment        (DNA-binding loop), (ii) β-core fragment and (iii) α-fragment.        FIG. 3B illustrates an example of construction of an analog        multiplier with three inputs. In the proposed circuit, the        cooperativity weights will be set by the binding reaction and        the analog promoters. When two subunits of T7 RNAp are regulated        with the same analog promoter, the cooperativity weight will be        doubled. This system demonstrates very low toxicity when cloned        in E. coli;    -   CRISPR, which is another synthetic biology system widely used to        regulate gene expression, was recently constructed to implement        an AND-logic gate. The CRISPR system consists of dCas9 protein        and small guide RNAs (sgRNAs), both of which have to be        expressed to function. In this research, we will exploit the        interaction between dCas9 and sgRNAs to build an analog        multiplier. This system has several advantages; (i) the system        can be used a repressor or activator when the dcas9 is fused to        the omega (w) subunit of RNAp, (ii) the sgRNA can be programmed        to interact with different genetic binding sites. In this case,        the binding efficiency of the interaction between the dCa9        protein and sgRNA can be programmed by running a random mutation        on the sgRNA sequence, which is considered a simple technique        for programming cooperativity binding. FIG. 3C shows a circuit        proposed for construction of an analog multiplier with        programmed cooperativity weights based on the CRISPR system.        Moreover, in this research we will use different methods to        generate libraries of split dCas9 protein into several subunits        (e.g., incremental truncation, multiplex inverse PCR and        others). There are some challenges in using CRISPR system. For        example, when dCas9 or sgRNA is combined with a strong promoter,        it might cause severe growth defects and toxicity to cells; and    -   Orthogonal O-ribosome, which is another synthetic biology system        that we will use to construct an analog multiplier. Recently, it        was applied to construct an AND logic gate with two inputs. The        system consists of two inputs that must be co-expressed to        receive a signal. One input will regulate the transcriptional        process, while the second will regulate the translational        process. We have applied this system in our lab and got        reasonable results (ratio between gene expression of high level        and low level ˜60 fold). In brief, the O-ribosome efficiently        and specifically translates its cognate orthogonal mRNA        (O-mRNA), which is not a substrate for the endogenous wild-type        ribosome.

All these systems will be very useful in scaling gene networks based onSMN architecture.

NF and PF Loop for Cooperativity Weight Fine Tuning

The simulation of the perceptgene (FIG. 1F) showed that small changes inthe cooperativity weight leads to large changes in the system function.Therefore, it is highly important to optimize the cooperativity weightof the perceptgene when building large-scale SMNs. To achieve that, PFand NF loops may be used. FIG. 3D shows that by altering the promoterbinding efficiency of the PF loop versus the shunt, we can tune the Hillcoefficient to different values. The same effect is achieved by alteringthe strength of the NF loop (data not shown).

Programing the Activation Function of Perceptgene

The threshold of the activation function in the perceptron orperceptgene mainly sets the “0” and “1” logic levels of the analoginputs. Moreover, its value significantly impacts signal propagation inANNs or AMNs, system performance, noise margin and system resourceconsumption. For example, a system with a low threshold and lowcooperativity weights can achieve the same performance of a system witha high threshold and high cooperativity weights. However, the firstsystem consumes fewer resources than the second. Thus, it may beadvantageous to control the threshold of the perceptgene activationfunction. To this end, three synthetic biological systems may be usedwhich exploit a competition between parts: (i) competition betweenpromoters, (ii) competition between proteins and (iii) competitionbetween binding sites. FIG. 3E shows two promoters that are located inopposite orientation to each other. Experimental results (FIG. 3E) showsthat there is interference between the convergent promoters, whichcauses a shift in the threshold or effective dissociation constant.Transcriptional interference between convergent promoters has beenreported in biology. The next system will be based on competitionbetween transcription factors and dCas9 on the same binding site. Thissystem is expected to shift the threshold as a function of dCas9 level.The dCas9 protein can be programmed to bind to any binding site thatincludes a specific DNA sequence called PAM. In this way, the samepromoter can be used with different dissociation constants. The samebehavior can be achieved by competition between the Sigma and anti-Sigmafactors. These systems have only three, rather than four, thermodynamicstates: (i) No transcription factors are bound, (ii) only the inputtranscription factor-RNA polymerase complex is bound and (iii) only thecompetitor transcription-RNA polymerase complex is bound. This simplemodel shows a shift in the threshold value as a function of thecompetitor protein level. The latter system is based on a recombinaseprotein and decoy binding sites. Recently, it has been shown thatrepetitive stretches of DNA that contain transcription factor bindingsites, can sequester transcription factors and act as a decoy, yieldingan increase in the effective dissociation constant of input-to-outputtransfer functions. A PhiC31 unidirectional serine recombinase was used,which targets its own cognate pair of non-identical recognition sites,known as attB and attP. PhiC31 can irreversibly invert or excise DNA onthe basis of the orientation of the surrounding pair of recognitionsites. The inverted recognition sites are known as attL and attR. Thesystem consists of:

-   -   phiC31 cloned under the control of the mutated P_(lux)        linearization circuit to achieve fine-tuned gene expression with        a broad region of linearity. To ensure low basal transcription        levels in the absence of input (AHL), there was added an ssrA        degradation tag (AAV) to PhiC31 recombinase proteins;    -   a constitutive promoter proD, which regulates the expression        level of the inverted green fluorescent protein gene (gfp),        which is located between the two recognition sites attB and        attP, and is cloned on a single copy number plasmid backbone BAC        (FIG. 3F). In the absence of PhiC31, proD regulates the inverted        gfp gene, that gives a background GFP signal (very low GFP). In        the presence of PhiC31 within the cell, the PhiC31-attB and        PhiC31-attP complexes flip the inverted gfp gene, such that it        will be in the same orientation as the proD promoter, resulting        in a high GFP signal. A ribozyme-based insulator component        (RiboJ) was added to the 5′ UTR of the gfp gene to reduce the        background signal; and    -   Decoy binding sites to sequester the PhiC31 recombinase protein.        This was achieved by introducing the two inverted recognition        sites, attL and attR, into medium and high copy number plasmids        (MCP and HCP), shifting the AHL-to-GFP transfer function (FIG.        3F).        A Perceptgene with a Negative Weight

ANNs often include positive and negative weights. For example, toconstruct the XOR logic gate (exclusive operation), three layers of aperceptron with negative and positive weights need to be cascaded.Therefore, in some embodiments, a perceptgene may be built in livingcells with negative weights (x^(−n)). This is achieved by applying twomethods. The first one is based on integration of repressors in ananalog multiplier, to yield an analog divider rather than analogmultiplier. The second method is based on controlling the threshold. Byreviewing equation 3 above, it can be seen that a negative weight can beimplemented by controlling the threshold of the perceptgene by thesystem inputs. Two methods to achieve this goal have been describedherein above.

SMNs with Emergent Cooperative Analog Computational and EvolutionaryAbilities

FIG. 4A shows one example of mapping an ANN to an SMN, and vice versa.By mapping the complex biochemical reaction network (FIG. 4A) to alinear domain, the function of this network can be simplified as alinear classifier (FIG. 4B) using three inputs with different weights(“1” if w_(x)·S_(x)+w_(y)·S_(y)−w_(z)·S_(x)>Cosnt, “0” otherwise). Thethreshold constant is set by the forward and reverse rates of thebio-enzymatic reaction. PF and NF loops are used to tune the weights1≤w_(x)≤2, 3≤w_(y)≤4 and 1≤w_(z)≤2. Below, it will further be shown thatSMNs can be integrated into more complex networks to build large-scalebiological systems with minimal requirements of host cell resources.These are intelligent parallel processing units that can executesophisticated computational and learning (evolutionary) functions inliving cells and electronics. Details about the construction of thesesystems will be provided after first establishing the theoreticalframework for mapping SMNs and biological systems to ultra-low powerelectronics. Naturally, biological signals propagate through networkswith random fluctuations, which can be described by a Poisson process.FIGS. 4C and 4D show stochastic simulation results of two systems;perceptgene (two inputs that are fed into a log-linear activationfunction are multiplied), and perceptron (two inputs that are fed into alog-linear activation function are summed up). The simulation resultsshow that perceptron fails to act as a binary classifier (there are noclear “0” and “1” states—FIG. 4D) when intrinsic noise is added to thesystem. By contrast, a perceptgene has clear “0” and “1” states (FIG.4C).

Mapping Molecular Networks to Nanoelectronics

Neuromorphic engineering is a multidisciplinary field thatinterpolates/extrapolates principles of neural networks into/fromelectronics. For example, it has been shown that a BJT/MOS-subthresholdtransistor can mimic neural activity, and recently, it has been shownthat memristor can mimic synapses. Alternately, neural networks havebeen implemented in electronics to build intelligent systems for problemoptimization and classification (e.g., retina for object recognition,regression and computation). Similarly, in some embodiments, the presentinvention provides for a new framework, termed ‘cytomorphicelectronics,’ which aims to mimic the dynamic behavior of biologicalsystems in living cells using electronic circuits. The goal ofcytomorphic electronics is to study, predict and build synthetic andnatural biological systems by providing a reliable and rapid simulationframework. In some embodiments, cytomorphic may be a multidisciplinaryframework that translates principles of molecular networks toengineering, and vice versa, just as neuromorphic engineering has led toneuro-inspired engineered systems (adaptive artificial intelligentmixed-signals electronics circuits). As was shown above, thethermodynamic Boltzmann exponential equations describe the electron flowin the electronic subthreshold MOS transistor as well as molecular fluxin chemical reactions. This similarity suggests that log-domain analogcomputations in electronics can be mapped to log-domain analogcomputations in biology, and vice versa. Thus, trans-linear circuits insubthreshold MOS transistors can be utilized to mimic the behavior ofbiochemical reactions and genetic circuits. However, it is challengingto capture the random fluctuations of biochemical reactions that involvea very small number of proteins, such as a DNA-protein binding reaction,primarily because the number of electrons that flow in subthreshold MOStransistors is much higher than the number of proteins that are involvedin biochemical reactions in living cells. Therefore, stand-aloneartificial noise generation circuits for low SNR had to be constructed.Such circuits often involve many analog and digital circuits andincrease the design complexity of scaling cytomorphic integratedelectronics. To overcome this challenge, it is suggested to combinetranslinear circuits with Nanoelectronics. Herein, it will be shown thatmemristor devices can mimic the deterministic as well the stochasticdynamics of biochemical reactions and genetic circuits. Recently, it hasbeen shown that the rate of switching in memristor devices is determinedby the bias-dependent activation energy (voltage/current controlled),following Boltzmann statistics Γ=A·exp(−E_(g)(ν)/K_(B)T), while anincrease in voltage decreases the energy barrier. This simple analysisshows that the reaction time (τ_(reaction)) of protein binding to DNAand the delay time of switching memristor (τ_(switch)), follow a Poissondistribution. As a first-order analysis, in asymptotic boundaryconditions, the memristor can mimic the binding process of biochemicalreactions. For example, for low protein levels, the binding site isempty with minimum activity and for high protein levels, all the bindingsites are occupied, with maximum activity. In a similar fashion, when noprogramming voltage is applied on the memristor, the TiO₂ layer is emptyby ionic oxygen vacancies, with very low activity (the memristorconductance is very low), and when a high programming voltage is appliedon the memristor, the TiO₂ layer is occupied by ionic oxygen, withmaximum activity (the memristor conductance is very high). Thus, bindingreactions and memristor devices exhibit a non-linear, input-outputtransfer function, with two logic states—“0/1”. Moreover, the stochasticbehavior of biochemical reactions and switching memristors is similar.These analogies suggest that one can efficiently mimic large-scalegenetic-processing systems in biological networks on a hybridmemristor-analog-digital electronic chip.

Artificial Molecular Networks (AMNs) in Electronics

AMNs attempt to apply principles of molecular networks in electroniccircuit design, to yield novel biologically inspired robust, intelligentand energy-efficient systems. In some embodiments, the present inventionintegrates memristors and translinear circuits to design and fabricateultra-low power electronic circuits exploiting the computational powerof the perceptgene model (see equations 2 and 3 above). The basic AMNmodel consists of three parts:

-   -   Multiplication (binding reaction): Translinear circuit design        exploits the exponential current-voltage non-linearity        relationship in semiconductors to perform inherent/built-in        complex mathematical operations such as multiplication and        division. They enable powerful, ultra-low power analog circuit        analysis and synthesis framework. Translinear circuits perform        these complex computations without using differential voltage        signals and could feasibly be integrated into device-level        circuit design methodology. Translinear circuits can be        implemented by bipolar junction transistors (BJT) in design of        systems with high speed or by subthreshold CMOS transistors in        design of ultra-low power systems. The output current (I_(out))        is given by:

$\begin{matrix}{I_{out} = \frac{I_{i_{1}} \cdot I_{i_{2}}}{I_{Ref}}} & (4)\end{matrix}$

-   -   (ii) Power-law function (Cooperativity weight): The simplest way        to interpolate the power law function into our analog        translinear circuits is by adding a resistive divider to these        circuits. When R₁ and R₂ are very large, very small currents        will pass through the resistors compared to the currents that        pass through the transistors. Thus, the output current (I_(out))        can be written as:

$\begin{matrix}{{I_{out} = {I_{T} \cdot \left( \frac{I_{in}}{I_{Ref}} \right)^{n}}},{n = \frac{R_{1} + R_{2}}{R_{2}}}} & (5)\end{matrix}$

-   -   The main advantage of using memristors to implement        cooperativity weight (or Hill coefficient) lies in the control        of the Hill coefficient values online, and in this case,        intelligent and adaptive electronics can be trained by machine        learning algorithms. Moreover, because the Hill coefficient is        set by the ratio of the resistors, high resistance can be used,        and in this case a small amount of power will be dissipated on        the resistors.    -   Log-linear activation function: It is simple to show that        Michaelis-Menten kinetics (Equation 2) can be modeled by        Kirchhoff's voltage law (KVL) or kickoff current law (KCL) and        by a voltage divider between resistances of value Y and K_(d).        In this circuit, the number of programming pulses (# P) controls        the memristance and represents the concentration of        transcription factors. The second memristor represents the        dissociation constant K_(d) (in this case, it will be initially        programmed to have a constant value). The power supply voltage        represents the maximum activity of the promoter (P_(ON)). The        voltage that is dropped on the capacitor in steady state        represents the bound promoter and is given by:

$\begin{matrix}{{V_{\Pr} = {V_{Pon} \cdot \frac{R_{y}}{R_{y} + R_{Kd}}}},{R_{y} = {f\left( {\# P} \right)}}} & (6)\end{matrix}$

The first Equation of 6 represents KVL and the second equationrepresents memristor flux-charge integration characteristics, while thefunction ƒ depends on memristor structure/physics features and programpulse waveform distribution. This circuit has several advantages: (i)the statistical distribution of a switching memristor device exhibits aPoisson distribution after each switching event, thus, it can capturethe stochastic dynamics of biochemical reactions. (ii) It provides for aprogrammable dissociation constant for design of large-scale-AMNs. Theother option of building a log-linear activation function is to use adifferential subthreshold CMOS translinear circuit. The output current(I_(Pr)) represents the bound promoter and is given by:

$\begin{matrix}{I_{\Pr} = {I_{Pon} \cdot \frac{I_{Y}}{I_{Y} + I_{Kd}}}} & (7)\end{matrix}$

To capture the stochastic behavior of genetic circuits, the differentialsubthreshold CMOS translinear circuit may be combined with a memristor,using a current mirror circuit.

Adaptive Genetic and Electronic Networks forIntelligent-Parallel-Computation

Machine learning is the science of getting artificial machines to actintelligently without being explicitly programmed. In the past decade,machine learning-based ANNs have been attracting vast attention aspotential new architectural components and models for computing a widevariety of problems, such as pattern classification, object recognition,image processing, signal processing and optimization solving. One of thekey elements of ANN is its ability to learn. A neural network is acomplex adaptive system, meaning it can change its internal structurebased on the information flowing through it. Typically, this is achievedthrough the weights adjustment, based on a first-order optimizationalgorithm that tends to converge to the global minimum of the gradientdescent of the mean square error metric function.

A Learning and Adaptation Model in AMNs and SMNs (Supervised Learning)

An innovative learning algorithm can be developed based on a perceptgeneabstract model. Based on this, SMNs and AMNs can build adaptivebiological systems with supervised evolutionary abilities, as well asartificial, intelligent ultra-low power, bioinspired translinearelectronic circuits for a new era of robust big data computing. In someembodiments, the present learning algorithm is based on two features:(i) computation of the perceptgene depends on the cooperativity weightsand therefore, by adjusting their values (Hill coefficient), a widerange of possible target output can be obtained for specific inputs, and(ii) the training rule minimizes the output error, using its gradientdescent in a log-linear domain. The perceptgene-based learning algorithmis shown in FIG. 5A and is given by the following equations:

$\begin{matrix}{E_{i} = {{\frac{1}{2} \cdot \left\lbrack {{\ln \left( y_{i} \right)} - {\ln \left( Y_{Di} \right)}} \right\rbrack^{2}} = {\frac{1}{2} \cdot \left\lbrack {\ln \left( \frac{y_{i}}{Y_{Di}} \right)}^{2} \right\rbrack}}} & (8)\end{matrix}$

Equation (8) calculates the error between the desired data (Y_(D)) andthe actual perceptgene output (y), before the activation function i,using the least-mean square rule in a log-linear domain (E_(i)=0 wheny_(i)=Y_(Di)). Then, the desired function will be achieved by adjustingthe values of cooperativity weight based on:

$\begin{matrix}{n_{ij}^{\prime} = {n_{ij} - {{\ln \left\lbrack \left( \frac{y_{i}}{Y_{Di}} \right)^{\lambda} \right\rbrack} \cdot {\ln \left( \frac{x_{j}}{K_{j}} \right)}}}} & (9)\end{matrix}$

Equation (9) calculates the new value of cooperativity weights (n′_(ij))based on the old value (n_(ij)) and gradient descent rule(−λ·dE_(i)/dy_(ij)=−λ·[dE_(i)/dy_(i)]·[dy_(i)/dn_(ij)]). j is an indexnumber of inputs, λ is a learning_(rate), and K_(j) is a normalizationparameter. The importance of equations (8) and (9) is the capacity toregulate the weight update by smaller steps, ensuring high resolutionand guarantee of a global minimum in tradeoff with training time andnumber of samples. These equations can also be applied in multilayerperceptgenes to describe more complex dynamics. This novel update rulemay be called the adaptive logarithm linear gene (Adalogline) algorithm,analogous to the Adaptive linear neuron (Adaline) algorithm, used inadaptive signal processing and control. The Adalogline algorithm can besimply implemented in synthetic biology (binding reactions, bindingcooperativity and gene regulation), translinear electronics circuits(multiplication, power law and KVL). Moreover, it has been shown thatthe log-transformed ratio of two input inducers can be achieved usinganalog synthetic biology. As a first step, the Adalogline was comparedto the Adaline algorithm, which is widely used in machine learning,based on the perceptron model. FIGS. 5B and 6C show a 2-input OR-logicgate constructed with a perceptron and perceptgene, respectively. It wasassumed that synaptic/cooperativity weights of theperceptron/perceptgene, and that it will be trained in a supervisedmanner to learn the logical OR function based on the information flowingthrough it and by desired labels. To achieve that, Adaline was ran onthe perceptron and Adalogline on the perceptgene, with the same learningrate and dataset. The simulation results (FIG. 5D) show that bothalgorithms required the same number of iterations to reach the targetweight values (with ˜zero error). In the next step, an intrinsic noisewas added to the output of the perceptron/perceptgene (z+Δz), that wasuniformly distributed between [0-1]/[1-10] or alternatively, was Poissondistributed (Δz²/z=1). FIG. 5E shows that the perceptron model-basedAdaline algorithm becomes oscillating/divergent when noise is added. Bycontrast, the perceptgene model-based Adalogline algorithm wassuccessfully trained when noise was added and acted as an OR logicfunction. The main reason for this behavior is that the perceptgenemodel is based on a logarithm function, which has a memory property,where the change depends on the history of the system (dy/y=dx/x), whilethe perceptron model is based on a linear relation without memory(dy=dx). This is a very important feature rendering the perceptgenemodel and Adalogline algorithm the best candidates to be applied inbiological systems and in noise-tolerant analog electronics systemswhere noise is present. In some embodiments, the perceptgene model andAdalogline algorithm may be configured for building an adaptivelog-linear classifier in living systems and electronics, based upon thefollowing stapes:

-   -   (i) Construct a single layer of SMN, based on the above, that        can be trained. PF and NF loops will be used to control the        values of the cooperativity weight. The training will be        performed offline, in-situ, as a first step and then online by        using a microfluidics, photodetector electronic circuit, and        computer to adjust the values of cooperativity weight based on        the Adalogline algorithm. In some embodiments, a single layer of        SMN may be constructed to be trained in vivo using the Cas9        system and analog synthetic biology circuits. The Cas9 will bind        and mutate PF and NF promoters. This will change the promoter        binding efficiency, that will lead to changes in the values of        the cooperativity weights; and    -   (ii) fabricate AMNs, based on above, that can be trained online.        By replacing the resistors with memristors, the values of        cooperativity weights can be adjusted based on the Adalogline        algorithm. Memristors have been successfully integrated with        analog CMOS and trained online using gradient descent update        rule for neuromorphic computing. The integration of memristors        and translinear circuits based on subthreshold CMOS technology        can be challenging, and as an alternative, BJT transistors may        be used. As a first step, a Cadence simulation will be using        0.18 um TowerJazz technology. The power estimation of N-input        perceptgene is 0.2 μW·N², by contrast, the power estimation of        N-input perceptron based on operational amplifier is 200 μW·N²        (we used 0.18 um TowerJazz technology).        SMNs and AMNs with Parallel Computational Abilities Using        Hopfield Networks

Recurrent ANNs have been proposed as a model to construct asynchronousparallel computing networks (Hopefield networks). In this model, eachperceptron behaves as an elementary unit that is fully cross-connectedby symmetric weight feedbacks, allowing bidirectional data traversal tothe rest of the ensemble. Hopfield networks have been proposed to solveseveral complex tasks that require massively parallel and compactcomputing processors with few parts such as: analog-to-digitalconversion, NP-complete problems (Traveling-Salesman Problem) andcontent addressable memories (associative). A perceptgene model can beused to build parallelly-interconnected ultra-low power electronics, aswell as to scale the computational complex dynamics of syntheticbiological systems based on the Hopfield paradigm. Hopfield networks areenergy-based that recursively converge to optimum in steady state. Insome embodiments, the perceptgene model has energy features similar tothose of a perceptron within a Hopfield network, termed a HopfieldMolecular Network (HMN). FIG. 6A shows a basic structure of HMN withthree nodes. The three nodes are fully connected with n_(ij) weights. Inearly works on Hopfield networks, it was shown that withoutauto-feedback and symmetric weight interconnections (n_(ij)=n_(ji)), theequations of the network dynamic motion could describe convergence tostable states, in which the output of all neurons (in our case, theoutput of the genes) remain constant without oscillations. As a firststep, an energy function based on the perceptgene model must beintroduced to harness the theoretical complexities posed by such anapproach, equivalent to ANNs (perceptron). Analogous to the Hopfieldanalytic model, the power consumption formula of an elementary circuit(FIG. 6B) of an AMN may be extracted to formalize the Hopfield energyfunction of perceptgene is

$\begin{matrix}{E_{i} = {{- \frac{K_{B}T}{q}} \cdot \left\lbrack {{\sum\limits_{i = 1}\; {I_{i} \cdot {\ln\left( {\prod\limits_{j = 1}\; \left( \frac{I_{j}}{I_{ref}} \right)^{n_{ij}}} \right)}}} - {\sum\limits_{i = 1}{I_{i} \cdot {\ln \left( \frac{I_{i}}{I_{ref}} \right)}}}} \right\rbrack}} & (10.1) \\{{\Delta \; E_{i}} = {{{- \frac{K_{B}T}{q}} \cdot \Delta}\; {I_{i} \cdot \left\lbrack {{\ln\left( {\prod\limits_{j = 1}\; \left( \frac{I_{j}}{I_{ref}} \right)^{n_{ij}}} \right)} - {\ln \left( \frac{I_{i}}{I_{ref}} \right)} - 1} \right\rbrack}}} & (10.2)\end{matrix}$

where q is an electron charge, I_(i) is a current that flows through Mitransistor and represents the input signal of perceptgene unit i, I_(j)is a current that flows through the Mj transistor and represents thefeedback signal of other perceptgene j units, i_(Ref) is normalizationcurrent, and n_(ij) is the Hill coefficient between perceptgene i andperceptgene j (equation 5). Equation (10.1) exactly fits the energyfunction that was developed in Hopfield networks in a log-linear domain(Translinear circuits). Equation (10.2) describes the change in theenergy due to change in the input. Thus, the model for altering L causesE to be a monotonically decreasing function. States recursive changewill continue until an optimal E is reached. This can be viewed byevaluating the motion equations of the circuit in FIG. 6B:

$\begin{matrix}{{{C \cdot \frac{{du}_{i}}{dt}} + \frac{u_{i}}{R}} = {\frac{K_{B}T}{q} \cdot \left\lbrack {{\ln\left( {\prod\limits_{j = 1}\; \left( \frac{I_{j}}{I_{ref}} \right)^{n_{ij}}} \right)} - {\ln \left( \frac{I_{ext}}{I_{Ref}} \right)}} \right\rbrack}} & (11)\end{matrix}$

The circuit will reach stable steady state when equation (11) equalzero, and by fitting the external current (i_(ext)), we will getΔE_(i)=0. The energy function of the Hopfield neural/molecular network,which is considered to be a Lyapunov function, describes the macroscopicdynamics of the network. It characterizes the energy minimizationprocess and convergence of the network from an initial state to aminimum energy steady state. By defining an optimization equation for aspecific application and reordering it in an energy-like style, thecorresponding weights that fit the network specifications andapplication demands can be extracted. The main advantage of the newnetwork (HMN) compared to the Hopfield neural network (based onperceptron), lies in the inherent implementation of the Boltzmannmachine system using the stochastic dynamics of subthresholdtransistors, memristor and genetic circuits. Due to the nature of theenergy function, the solution of the Hopfield network is highlydependent on its initial state. Unfortunately, the energy function maydecrease and then settle to one of the equilibrium points called a“local minima” that does not correspond to the correct state. However,stochastic recurrent networks (when noise is added to Hopfield networkssimilar to our systems) could avoid this situation because stochasticdynamics can provide energy to the system resonating it to the globalminimum. Thus there can be built:

-   -   (i) A log-linear 4/8-bits analog-to-digital converter (ADC)        using AMNs (electronic) based on HMN design (FIG. 6C).        Biological and physiological signals often have a log-linear        input-output transfer function. Therefore, ADC that can directly        convert the measured analog signal in a logarithm domain to a        digital signal will improve the performance of biomedical        devices. It has shown that the Hopfield energy function        satisfies the ADC problem in a linear-linear domain with        connection weights 2^(i+j), however, it failed to solve the ADC        problem in a log-linear domain. By contrast, our new Hopfield        energy function (Equation 10) inherently satisfies the ADC        problem in a log-linear domain with connection weights i+j. In        our ADC design, all the inputs of the HMN are connected to the        same analog input. The second advantage of the proposed HMN is        that the ratio of the maximum and minimum coefficients is small        compared to the original Hopfield network. The Hopfield neural        and molecular network for ADC, recursively solved evolving from        initial state and converge to digital steady state (FIG. 6D        compares the energy function between two different analog        inputs). There can be built an ultra-low power analog        supercomputer, with parallel computational and adaptive        abilities, to solve complex stochastic cognitive tasks in real        time with high precision. Alternatively, asymmetric Hopfield        networks may be applied based only on feed-forward topologies;        and    -   (ii) content addressable memory (CAM) using SMNs (in living        cells) based on HMN design. The construction of biological        systems in living cells with memory abilities has recently        gained widespread attention for its potential in new        biotechnology and biomedical applications as well as to study        systems biology. So far, living cells with two states have been        successfully constructed using positive feedback loops (e.g.,        the toggle switch). To go beyond this, the fact that the        Hopfield energy function guarantees convergence to local minima        may be used, and therefore, the HMN network can serve as a        system that can store pattern with an associative memory        element, co-localizing memory and computation. The new HMN        design may be used to construct biological systems in living        cells with memory abilities of three rather than two states, and        investigate computation within memory, utilizing associative        processing capacities.

Scaling Gene Networks in Living Cells Based on a Log-Linear ThresholdUnit Model:

The early works of ANNs were based on a linear threshold unit (LTU) andwere specifically targeted to serve as a computational model of the“nerve net” in the brain. The LTU model consists of two parts; (i)digital-to-analog converter (DAC) which sums all the inputs and (ii) anADC that converts the analog signals to digital outputs by designing thedifferent shapes of the activation function. It has been shown that theLTU model can implement any Boolean logic function. For example, AND/ORlogic gates can be implemented by a simple perceptron, by varying thethreshold values (FIG. 7A). An XOR logic function can be implemented byconstructing a band pass (FIG. 7B) through cascading two perceptronlayers. In some embodiments, a perceptgene model and SMNs may be used tobuild a log-linear threshold unit (L²TU) for scaling gene networks inliving cells with a minimal number of synthetic parts. The inputs andoutputs are binary discrete numbers, the weights are unchanged, with noengineering role and a more flexible threshold value. The L²TU is analternative biodesign model to the conventional Boolean algebra modeland is based on analog and digital design rules. In analogous to LTU,the L²TU consists of two parts: (i) linear-log DAC, which multiplies thedigital inputs together and (ii) a log-linear ADC that converts theanalog signals to digital outputs by designing its activation function.In some embodiments, two examples for constructing complex logicfunctions based on the L²TU model may be configured:

-   -   (i) Scaling a full-bit adder: First, there will be constructed a        1-bit full adder that has three inputs: A, B and Carry in        (C_(in)), and two outputs: Sum and Carry out (C_(out)). The        truth table of a 1-bit full adder is shown in FIG. 7B. The        analog signal is the multiplication of the digital inputs        (A·B·C_(in)) that have features of analog signals such as        current or molecular concentration. By presenting the digital        output signals (Sum & C_(out)) as a function of the analog        signal (A·B·C_(in)), one can observe the activation function of        every output (FIG. 7C). For example, the Cout output can be        viewed as a high pass filter with a threshold of 100 a.u., and        the Sum output is a combination of the band pass (10-100 a.u.)        and high pass filters with a threshold of 1000 a.u. The full        construction of a 1-bit full adder is presented in FIG. 7D.        Hybrid promoters and proteins binding reactions will be used to        implement a log-linear DAC. FIG. 7E shows an example of        construction of a 2-inputs-log-linear DAC using the lacI/tetR        hybrid promoter in living cells. The log-linear DAC acts as an        analog multiplier when the inputs accept digital values. The        design and construction of the log-linear ADC is more        challenging than of the DAC. In some embodiments, the analog        circuit design discussed above may be utilized and combined with        the digital circuit design discussed above, to engineer the        shape of the activation function achieving a log-linear ADC        processor. The new circuit will rely on a hybrid analog-digital        design and mixed signal. FIG. 7F shows a two-component genetic        circuit for construction of a low/high/band pass filter with        programmable threshold values: (I) a wide dynamic range circuit        based on graded PF that accepts AHL as an analog input and        controls the expression level of LuxR and AraC in analog        fashion, (II) an ADC processor. A band pass was achieved using        competition between P_(BAD) and P_(lux), both of which are        controlled with the AHL input (FIG. 7G). The same circuit can        behave as a high pass filter, with a very high threshold value        when the gfp signal that is controlled by P_(lux) is read rather        than P_(BAD). For high AHL concentrations, the P_(lux) promoter        wins the competition and leads to a signal in the 3-5′ direction        (FIG. 7G). A low pass filter has been achieved by competition        between a constitutive promoter and the P_(lux) promoter (FIG.        7G). Note that cloning the promoters in different copy numbers        can increase/decrease the threshold values (data not shown).        Furthermore, adding decoy binding sites of P_(BAD) and P_(lux)        will affect the transfer function. Quorum sensing cell-to-cell        communication may be used to wire the DAC and ADC. This        mechanism has been widely used in synthetic biology. For        example, a bacterial sender strain was constructed that        constitutively produces AHL molecules and we combined them with        a bacterial receiver strain that includes a band pass filter        based on P_(lux) promoter in the same solution medium (FIG. 7H).        Equivalently, the DAC will produce AHL molecules by replacing        the gfp gene with luxI gene and the ADC will accept the AHL        molecules.    -   (ii) 4-input XOR gate: this may be achieved by combining a        4-bits log-linear DAC and a log-linear ADC processor that        consists of two shifted band pass circuits. The main advantage        of the L²TU biodesign framework compared to other frameworks, is        that fewer devices are needed to carry out a given computation        with minimal requirements of host cell resources (1-bit full        adder will require only 5 synthetic parts, and a 4-input XOR        will require 6 synthetic parts), and at the same time, the        output results are as reliable as in the digital biodesign        framework. In some embodiments, a biocomputer may thus be built,        which includes the basic Arithmetic-logic operations (e.g.,        4-bit full Adder, 4-bit Subtractor, and logic gates) and memory,        that operates across living cells with a minimal number of        synthetic parts and minimal requirements of host cell resources,        to solve complex tasks in real time with high precision. The        proposed biocomputer can operate as an embedded system or can be        integrated with bioelectronics to perform biomarker analysis for        diagnostic and therapeutic applications (e.g, detect and respond        to changes in the state of health). In some embodiments, the        intelligent genetic systems discussed above may be combined with        stress promoters, e.g., to detect toxins in water.

The Architecture of Biological Systems to Scale-Up SMNs and AMNs

FIG. 8A illustrates the number of protein subunits (n) in E. coli. FIG.8A shows that the distribution of odd number protein subunits (n=1, 3, 5. . . ) follows Poisson statistics, which indicates that most nodes haveapproximately the same number of links. Such networks are known as arandom network. By contrast, the distribution of even number proteinsubunits (n=2, 4, 6, . . . ) is characterized by a power-law degreedistribution, termed Scale-free networks. It has been shown that manybiological networks are characterized as a scale-free networks. In suchnetworks, the probability that a node is highly connected isstatistically more significant than in a random network. This providesrobustness to the network. Moreover, in some embodiments, the presentinvention provides for an informative model that fits power-lawdistribution based on an analog-digital processing unit using theShannon theorem (FIG. 8A). In this model, the quantitative Fig. of Merit(evaluates performance, speed and energy) of a perceptgene isapproximated in the presence of intrinsic noise. It is assumed that theintrinsic noise follows Poisson statistics (FIG. 8B). Both modelsindicate that cells optimize considering an overwhelming tradeoffbetween power, speed and precision. In some embodiments, this model maybe further tested for other organisms and used to scale-up the design ofsynthetic biological and electronic systems.

In some embodiments, the present invention merges many new andinnovative ideas from neuroscience, systems biology and electricalengineering, to offer a novel framework for collective computationalintelligent abilities, as detailed in table 1 below. This frameworknaturally presents in synthetic biological and translinear electronicsystems. The present approach is supported by several preliminaryexperimental and theoretical results, and most importantly, it underliesthe analog synthetic biology and cytomorphic works. In some embodiments,Escherichia coli and yeast may be used as host cells for the circuits.Electronic circuits may be fabricated by TowerJazz Semiconductor.

TABLE 1 perceptron vs perceptgene properties and features FeaturesPerceptron Perceptgene Bio-inspired Brain Cell Biology Activation NeuronGene Regulation Connection Weighting Synapse (wij) Cooperativity Binding(nij) Operation Domain Linear Log-Linear Activation Function SigmoidHill-Function Collective Process Addition Multiplication GradientDescent learning rule${\Delta \; w_{ij}} = {\eta {\sum\limits_{j}{\left( {y_{ij} - d_{ij}} \right) \cdot x_{ij}}}}$${\Delta \; n_{ij}} = {\sum\limits_{j}{{\ln \left( \left( \frac{y_{ij}}{d_{ij}} \right)^{\eta} \right)} \cdot {\ln \left( x_{ij} \right)}}}$Noise tolrtance Training is Sensitive Training is Robust Change inEnergy${\Delta \; E_{i}} = {{- \Delta}\; {y_{i} \cdot {\sum\limits_{j \neq i}{w_{ij} \cdot y_{j}}}}}$${\Delta \; E_{i}} = {{- K_{B}}{T \cdot \Delta}\; {y_{i} \cdot {\ln \left( {\prod\limits_{j \neq i}\; \left( \frac{y_{j}}{y_{0}} \right)^{n_{ij}}} \right)}}}$Content-Addressable Hopfield Boltzmann Memory Network TopologyFeedforward/Recurrent Feedforward/Recurrent Causality None Weber's lawImplementation CMOS Mixed Signal Translinear circuits ActivationFunction Differential Amplifier KVL/KCL Connection Weighting MemristorMemristor Speed High High Power High Low Design Simple Complex

Experimental Results

As noted above, the present invention provides for a perceptgene-basedneural network. FIG. 9A illustrates a single neural cell, where I₁, I₂are the inputs, w₁, w₂ are input weights, φ is the activation function,and n is the iteration number. The perceptron algorithm functions asfollows:

v_(n) = w_(1, n)I₁ + w_(2, n)I₂ $y_{n} = \left\{ {{\begin{matrix}{0,} & {{v_{n} - Y_{th}} < 0} \\{1,} & {{v_{n} - Y_{th}} \geq 0}\end{matrix}E_{rr}} = {{\frac{1}{2}\left( {Y_{e\; {xp}} - y_{n}} \right)^{2}W_{i,{n + 1}}} = {W_{i,n} - {{\eta \left( {y_{n} - Y_{e\; {xp}}} \right)}I_{i}}}}} \right.$

whereas the perceptgene algorithm functions based on the following:

v_(n) = I₁^(w_(1, n))I₂^(w_(2, n)) $y_{n} = \left\{ {{\begin{matrix}{1,} & {\frac{v_{n}}{Y_{th}} < 3} \\{10,} & {\frac{v_{n}}{Y_{th}} \geq 3}\end{matrix}E_{rr}} = {{\frac{1}{2}\left( {\log \left( \frac{y_{n}}{Y_{e\; {xp}}} \right)} \right)^{2}W_{i,{n + 1}}} = {W_{i,n} - {\eta \; {\log \left( \frac{y_{n}}{Y_{e\; {xp}}} \right)}{\log \left( \frac{I_{i}}{2} \right)}}}}} \right.$

With reference to FIG. 9B, in some embodiments the present inventionprovides for a three-layer neural network comprising an input layerhaving N inputs, an intermediate layer having M neural cells, and anoutput layer having a single neural cell. In FIG. 9B, I₁, I₂, . . .I_(N) represent inputs, H₁, H₂, . . . H_(M) represent interim layersneural cells, and out is the output layer neural cell. V_(x) willrepresent the input of neural cell X, and O_(x) the output of neuralcell X.

In this configuration, a perceptron-based network may use the logisticactivation function

${\phi (v)} = \frac{1}{1 + {\exp \left( {- v} \right)}}$

The forward pass algorithm of this network will then be, generally:

$v_{H_{m}} = {\sum\limits_{k = 1}^{N}\; {w_{{N*{({m - 1})}} + k}*I_{k}}}$O_(H_(m)) = ϕ(v_(H_(m)))$v_{out} = {\sum\limits_{k = 1}^{M}{O_{H_{k}}*w_{{N*M} + k}}}$O_(out) = ϕ(v_(out))

And in the case of the network illustrated in FIG. 9B:

v_(H₁) = w₁ * I₁ + w₂ * I₂, v_(H₂) = w₃ * I₁ + w₄ * I₂$O_{H_{1}} = {{\phi \left( v_{H_{1}} \right)} = \frac{1}{1 + {\exp \left( {- v_{H_{1}}} \right)}}}$${O_{H_{2}} = {{\phi \left( v_{H_{2}} \right)} = \frac{1}{1 + {\exp \left( {- v_{H_{2}}} \right)}}}},{v_{out} = {{w_{5}*O_{H_{1}}} + {w_{6}*O_{H_{2}}}}}$$O_{out} = {{\phi \left( v_{out} \right)} = \frac{1}{1 + {\exp \left( {- v_{out}} \right)}}}$

The backpropagation algorithm of this network will be, for training raten, where

${E_{rr} = {\frac{1}{2}\left( {Y_{e\; {xp}} - O_{out}} \right)^{2}}},{\frac{\partial E_{rr}}{\partial w_{5}} = {\frac{\partial E_{rr}}{\partial O_{out}}\frac{\partial O_{out}}{\partial v_{out}}\frac{\partial v_{out}}{\partial w_{5}}}}$$\frac{\partial E_{rr}}{\partial O_{out}} = {- \left( {Y_{e\; {xp}} - O_{out}} \right)}$$\frac{\partial O_{out}}{\partial v_{out}} = {O_{out}\left( {1 - O_{out}} \right)}$$\frac{\partial v_{out}}{\partial w_{5}} = O_{H_{1}}$$\frac{\partial E_{rr}}{\partial w_{1}} = {\frac{\partial E_{rr}}{\partial O_{out}}\frac{\partial O_{out}}{\partial v_{out}}\frac{\partial v_{out}}{\partial O_{H_{1}}}\frac{\partial O_{H_{1}}}{\partial v_{H_{1}}}\frac{\partial v_{H_{1}}}{\partial w_{1}}}$$\frac{\partial v_{out}}{\partial O_{H_{1}}} = w_{5}$$\frac{\partial O_{H_{1}}}{\partial v_{H_{1}}} = {O_{H_{1}}\left( {1 - O_{H_{1}}} \right)}$$\frac{\partial v_{H_{1}}}{\partial w_{1}} = I_{1}$

After finding the partial derivatives of the weighted error, theweightings vector will be updated as follows:

$w_{i,{n + 1}} = {w_{i,n} - {\eta \frac{\partial E_{rr}}{\partial w_{i,n}}}}$

For the perceptgene-based network, the forward pass algorithm is,generally:

$v_{H_{m}} = {\prod\limits_{k = 1}^{N}\; I_{k}^{w_{{N*{({m - 1})}} + k}}}$O_(H_(m)) = ϕ(v_(H_(m)))$v_{out} = {\prod\limits_{k = 1}^{M}O_{H_{k}}^{w_{{N*M} + k}}}$O_(out) = ϕ(v_(out))

The same activation function as for the perceptron-based network may beused:

${\phi (v)} = \frac{1}{1 + {\exp \left( {- v} \right)}}$

whereby the function is illustrated in FIG. 9C. Both networks were runover a training set comprising 342 samples, with a verification set of114 samples. However, the classification by perceptgene would need to betagged by [1,10] rather than [0,1], to enable performing a logarithmicfunction. Accordingly, the activation function for perceptgene may bemodified as follows:

${\phi (v)} = 10^{\frac{1}{1 + {e\; {{xp}{({{- {lo}}\; g\; 10{(v)}})}}}}}$

The back propagation algorithm for the perceptgene network, for trainingrate n, will be:

$E_{rr} = {\frac{1}{2}\left( {\log \left( \frac{O_{out}}{Y_{e\; {xp}}} \right)} \right)^{2}}$$\frac{\partial E_{rr}}{\partial w_{5}} = {\frac{\partial E_{rr}}{\partial O_{out}}\frac{\partial O_{out}}{\partial v_{out}}\frac{\partial v_{out}}{\partial w_{5}}}$$\frac{\partial E_{rr}}{\partial O_{out}} = {{2*0.5*{\log \left( \frac{O_{out}}{Y_{e\; {xp}}} \right)}*\frac{1}{\frac{O_{out}}{Y_{e\; {xp}}}}*\frac{1}{Y_{e\; {xp}}}} = {{\log \left( \frac{O_{out}}{Y_{e\; {xp}}} \right)}\frac{1}{O_{out}}}}$$\begin{matrix}{\frac{\partial O_{out}}{\partial v_{out}} = \frac{\partial{\phi \left( v_{out} \right)}}{v_{out}}} \\{= {\frac{1}{v_{out}}*{\phi \left( v_{out} \right)}*{\log_{10}\left( {\phi \left( v_{out} \right)} \right)}*}} \\{\left( {1 - {\log_{10}\left( {\phi \left( v_{out} \right)} \right)}} \right)} \\{= {\frac{1}{v_{out}}*O_{out}*{\log_{10}\left( O_{out} \right)}*\left( {1 - {\log_{10}\left( O_{out} \right)}} \right)}}\end{matrix}$$\frac{\partial v_{out}}{\partial w_{5}} = {{O_{H_{2}}^{w_{6}}*O_{H_{1}}^{w_{5}}*{\log_{10}\left( O_{H_{1}} \right)}} = {{{v_{out}*{{\log_{10}\left( O_{H_{1}} \right)}--}} > \frac{\partial E_{rr}}{\partial w_{5}}} = {{{\log \left( \frac{O_{out}}{Y_{{ex}\; p}} \right)}\frac{1}{O_{out}}\frac{1}{v_{out}}*O_{out}*{\log_{10}\left( O_{out} \right)}*\left( {1 - {\log_{10}\left( O_{out} \right)}} \right)v_{out}{\log_{10}\left( O_{H_{1}} \right)}} = {{\log \left( \frac{O_{out}}{Y_{{ex}\; p}} \right)}{\log_{10}\left( O_{out} \right)}\left( {1 - {\log_{10}\left( O_{out} \right)}} \right){\log_{10}\left( O_{H_{1}} \right)}}}}}$$\frac{\partial E_{rr}}{\partial w_{1}} = {\frac{\partial E_{rr}}{\partial O_{out}}\frac{\partial O_{out}}{\partial v_{out}}\frac{\partial v_{out}}{\partial O_{H_{1}}}\frac{\partial O_{H_{1}}}{\partial v_{H_{1}}}\frac{\partial v_{H_{1}}}{\partial w_{1}}}$$\frac{\partial v_{out}}{\partial O_{H_{1}}} = {{w_{5}O_{H_{1}}^{w_{5} - 1}O_{H_{2}}^{w_{6}}} = {{w_{5}O_{H_{1}}^{w_{5}}O_{H_{1}}^{- 1}O_{H_{2}}^{w_{6}}} = {w_{5}O_{H_{1}}^{- 1}v_{out}}}}$$\frac{\partial O_{H_{1}}}{\partial v_{H_{1}}} = {\frac{1}{v_{H_{1}}}*O_{H_{1}}*{\log_{10}\left( O_{H_{1}} \right)}*\left( {1 - {\log_{10}\left( O_{H_{1}} \right)}} \right)}$$\frac{\partial v_{H_{1}}}{\partial w_{1}} = {v_{H_{1}}{\log \left( v_{H_{1}} \right)}}$

After finding the partial derivatives of the weighted error, theweightings vector will be updated as follows:

$w_{i,{n + 1}} = {w_{i,n} - {\eta \frac{\partial E_{rr}}{\partial w_{i,n}}}}$

The results of running both algorithms—perceptron and perceptgene—on thetraining set (using a training rate of n=0.5 and 10 neural cells in theintermediate layer) are given in FIGS. 9D-9G. FIGS. 9D-9E illustrate theerror rate as a function of iteration number for perceptron andperceptgene, respectively. FIG. 9F-9G illustrate the error rate as afunction of iteration number for perceptron and perceptgene,respectively, when noise is added. As can be seen, the perceptgenenetwork reaches error rates which are as low as those of perceptron. Inaddition, both algorithms do not show significant effect when noise isadded. Accordingly, it may be concluded that a perceptgene-based neuralnetwork may reach at least the performance levels of a perceptron-basednetwork.

In another experiment, the algorithm of the presentinvention—perceptgene—was tested against a perceptron-based algorithmusing the Modified National Institute of Standards and Technology(MNIST) database, based on a 400-300-10 configuration, a learning rateof 0.1 and 1000 iterations. The results are presented in FIG. 10 and intable 2 below:

TABLE 2 Learning rate 0.001 pg/0.01 pp (batch size = 1) 700X300X10 10exp(x)/1 + exp(x) 10 x/1 + x Perceptron Perceptgene [1, 10] AccuracyIterations Accuracy Iterations 100 — 10 60.2% 10 500 37.8% 83.7% 100043.9% 88.3% 5000 83.4% 93.9%

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electromagnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object-oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (for example, through the Internet using an Internet ServiceProvider).

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a hardware processor of a general-purpose computer,special purpose computer, or other programmable data processingapparatus to produce a machine, such that the instructions, whichexecute via the processor of the computer or other programmable dataprocessing apparatus, create means for implementing the functions/actsspecified in the flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

The flowcharts and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

In the description and claims of the application, each of the words“comprise” “include” and “have”, and forms thereof, are not necessarilylimited to members in a list with which the words may be associated. Inaddition, where there are inconsistencies between this application andany document incorporated by reference, it is hereby intended that thepresent application controls.

1. An analog signal processing circuit comprising: a first promoteroperably linked to a nucleic acid sequence encoding a first outputmolecule, wherein said promoter is responsive to a cooperative inputsignal comprising at least two cooperative inputs, and whereinexpression of said at least two cooperative inputs is tunable,optionally wherein the cooperativity of said at least two inputs istunable.
 2. (canceled)
 3. The analog signal processing circuit of claim1, wherein said promoter is a hybrid promoter comprising at least tworegulator binding sites.
 4. The analog signal processing circuit ofclaim 3, wherein a. at least one of said at least two regulator bindingsites binds an activator and at least one of said at least two regulatorbinding sites binds a repressor, b. said at least two inputs bind tosaid at least two regulator binding sites, or wherein said at least twoinputs bind to at least two regulators that bind to said at least tworegulator binding sites; or c. said at least two regulatory bindingssites are a LuxR binding site and a LacI binding site, optionallywherein said at least two inputs are acyl-homoserine lactone (AHL) andisopropyl β-d-thiogalactopyranoside (IPTG).
 5. (canceled)
 6. (canceled)7. (canceled)
 8. The analog signal processing circuit of claim 1,further comprising at least one of a. a second promoter operably linkedto a nucleic acid sequence encoding at least one of said cooperativeinputs, wherein said second promoter comprises a binding site for saidat least one of said cooperative inputs, optionally wherein said bindingsite in said second promoter comprises a modification that alters abinding affinity of said at least one cooperative input to said bindingsite relative to a binding affinity of said at least one cooperativeinput to an unmodified binding site; b. a third promoter operablylinking to a nucleic acid sequence encoding a second output molecule,wherein said third promoter is responsive to said first output molecule,optionally wherein said third promoter comprises a pBAD promoter, andsaid first output molecule is araC protein; c. arabinose; d. a regulatorsequence that regulates translation of said first output molecule and islocated between said first promoter and said nucleic acid sequenceencoding said first output molecule; optionally wherein said regulatorysequence is a riboswitch responsive to theophylline; and e. a regulatorysequence that regulates translation of said second output molecule andis located between said third promoter and said nucleic acid sequenceencoding said second output molecule, optionally wherein said regulatorysequence is a riboswitch responsive to theophylline.
 9. (canceled) 10.The analog signal processing circuit of claim 1, wherein a. a bindingaffinity to said first promoter of said at least two inputs, or said atleast two regulators bound to said inputs, is tunable; b. said at leasttwo cooperative inputs are at least two factors that share a commonbinding site and wherein said first promoter comprises said commonbinding site, optionally wherein said at least two factors that share acommon binding site are a Sigma factor and an anti-Sigma factor; or c.said analog signal processing circuit further comprises said at leasttwo factors than share a common binding site, or wherein said at leasttwo cooperative inputs are Cas9 and a small guide RNA (sgRNA),optionally wherein said tunability of said Cas9 and said sgRNA isdetermined by mutating said sgRNA sequence to alter a binding affinityof said Cas9 to said sgRNA.
 11. (canceled)
 12. (canceled)
 13. (canceled)14. (canceled)
 15. (canceled)
 16. The analog signal processing circuitof claim 1, wherein said first promoter is responsive to a protein orprotein complex consisting of more than one subunit, and wherein said atleast two cooperative inputs are at least two of said subunits; whereinsaid protein consisting of more than one subunit is selected from: a. T7RNA polymerase and said at least two cooperative inputs are analpha-fragment subunit of T7 RNA polymerase, a sigma-fragment subunit ofT7 RNA polymerase and a beta-core fragment subunit of T7 RNA polymerase,optionally further wherein the analog signal processing circuit furthercomprises a nucleic acid sequence coding for said alpha-fragmentsubunit, a nucleic acid sequence coding for said sigma-fragment subunitand a nucleic acid sequence coding for said beta-core fragment subunit,wherein said nucleic acid sequences coding for said T7 RNA polymerasesubunits are operably linked to at least one promoter and optionallywherein said nucleic acid sequences coding for said T7 RNA polymerasesubunits are operably linked to a plurality of promoters, wherein allthree nucleic acid sequences are not linked to the same promoter andwherein the cooperativity of the inputs is determined by the bindingaffinities of said plurality of promoters; and b. Cas9.
 17. (canceled)18. (canceled)
 19. (canceled)
 20. (canceled)
 21. (canceled) 22.(canceled)
 23. (canceled)
 24. (canceled)
 25. (canceled)
 26. The analogsignal processing circuit of claim 1, wherein said first promoteroperably linked to a nucleic acid sequence encoding a first outputmolecule further comprises a fourth promoter that transcribes in adirection opposite to a transcriptional direction of said firstpromoter, and wherein binding of at least one of said at least twocooperative inputs to said fourth promoter interferes with transcriptionfrom said first promoter.
 27. An analog signal processing circuitcomprising: a. a first tunable promoter operably linked to a nucleicacid sequence coding for a DNA recombinase; b. a second constitutivepromoter operably linked to a nucleic acid sequence that when invertedcodes for a first output molecule and wherein said nucleic acid sequenceis flanked by recognition sites for said DNA recombinase; and c. decoyrecognition sites for said DNA recombinase, wherein said decoy sites arewithin: i. a nucleic acid molecule comprising (a), ii. a nucleic acidmolecule comprising (b), or iii. a third nucleic acid molecule.
 28. Theanalog signal processing circuit of claim 27, wherein said tunablepromoter comprises a Plux binding site, and is tunable by addition ofAHL.
 29. (canceled)
 30. (canceled)
 31. (canceled)
 32. (canceled)
 33. Acell comprising the analog signal processing circuit of claim
 1. 34. Amethod for converting an analog signal into a digital output, comprisingcontacting the analog signal processing circuit of claim 1, with said atleast two inputs and detecting said first output molecule, said secondoutput molecule, or both thereby converting an analog signal into adigital output.
 35. The method of claim 34, wherein said detectingcomprises quantification of said output molecule.
 36. The method ofclaim 34, wherein said digital output is either a positive or a negativeoutput optionally wherein said method further comprises tuning athreshold for converting said analog input into a positive digitaloutput wherein said tuning comprises at least one of: i. tuningexpression of at least one of said at least two regulators; ii. tuning abinding efficiency of at least one of said at least two inputs to abinding site; iii. tuning a binding efficiency of at least one of saidat least two regulators to a binding site; iv. adding a molecule thatbinds to said regulatory sequence, wherein said molecule that binds saidregulatory sequence is theophylline; and v. adding a molecule that bindsto said first output molecule and alters binding of said first outputmolecule to said third promoter, wherein said molecule that binds tosaid first output molecule is arabinose.
 37. (canceled)
 38. (canceled)39. (canceled)
 40. (canceled)
 41. A system comprising: at least onehardware processor; and a non-transitory computer-readable storagemedium having stored thereon program instructions, the programinstructions executable by the at least one hardware processor toexecute a genetic-type machine learning algorithm configured for:receiving a sequence of inputs, wherein each of said inputs has anassociated weight, operating a neural network to generate, as output, aweighted multiplication of said inputs, calculating an error valuebetween said output and a target output, and adjusting the values of oneor more of said weights based on said error value and a specifiedlearning rate, wherein said adjusting is determined, at least in part,based on a log-linear gradient descent training rule.
 42. The system ofclaim 41, wherein said hardware processor is a DNA-based processor. 43.The system of claim 41, wherein said algorithm is further configured torepeat iteratively said steps of operating, calculating, and adjusting,until said error value is less than a specified threshold.
 44. Thesystem of claim 41, wherein said neural network comprises a plurality oflayers.
 45. The system of claim 44, wherein said adjusting furthercomprises backpropagating said gradient descent through said pluralityof layers, using the chain rule derivatives.
 46. The system of claim 41,wherein said calculating comprises determining a mean square errorvalue.
 47. The system of claim 41, wherein said learning rate is anadaptive learning rate. 48-61. (canceled)